Write the first terms of each of the following sequences whose nth term are:
an = 3n + 2
an = (n – 2)/3
an = 3n
a_{n}=\frac{3 n-2}{5}
an = (-1)n2n
an = 2n2 – 3n + 1
an = n(n – 2)/2
an = (2n – 3)/ 6
an = n2 – n + 1
Show that the sequence defined by an = 5n – 7 is an A.P., find its common difference.
Show that the sequence defined by an = 3n2 – 5 is not an A.P.
The general term of a sequence is given by an = -4n + 15. Is the sequence an A.P.? If so, find its 15th term and the common difference.
For the following arithmetic progressions write the first term a and the common difference d:
– 5, -1, 3, 7,…
1/5, 3/5, 5/5, 7/5,…
0.3, 0.55, 0.80, 1.05,…
-1.1, – 3.1, – 5.1, – 7.1,…
Write the arithmetic progression when first term a and common difference d are as follows:
a = 4, d = – 3
a = –1, d = 1/2
a = –1.5, d = – 0.5
In which of the following situations, the sequence of numbers formed will form an A.P.?
The cost of digging a well for the first metre is Rs 150 and rises by Rs 20 for each succeeding metre.
The amount of air present in the cylinder when a vacuum pump removes each time 1/4 of their remaining in the cylinder.
Divya deposited Rs 1000 at compound interest at the rate of 10% per annum. The amount at the end of first year, second year, third year, …, and so on.
Find:
10th term of the AP 1, 4, 7, 10….
18th term of the AP √2, 3√2, 5√2, …….
nth term of the AP 13, 8, 3, -2, ……….
10th term of the AP -40, -15, 10, 35, ………….
8th term of the AP 11, 104, 91, 78, ……………
11th term of the AP 10.0, 10.5, 11.0, 11.2, …………..
9th term of the AP 3/4, 5/4, 7/4 + 9/4, ………..
Find the 12th term from the end of the following arithmetic progressions:
1, 4, 7, 10, … ,88
Which term of the AP 84, 80, 76, … is 0?
Which term of the AP 4. 9, 14, …. is 254?
Which term of the AP 21. 42, 63, 84, … is 420?
Which term of the AP 121, 117. 113, … is its first negative term?
Is 68 a term of the A.P. 7, 10, 13,… ?
Is 302 a term of the A.P. 3, 8, 13, …. ?
Is -150 a term of the A.P. 11, 8, 5, 2, … ?
How many terms are there in the A.P.?
7, 10, 13, ….., 43
-1, -5/6, -2/3, -1/2, … , 10/3
7, 13, 19, …, 205
18, 15½, 13, …., -47
The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
If 9th term of an A.P. is zero, prove its 29th term is double the 19th term.
If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.
The 10th and 18th terms of an A.P. are 41 and 73 respectively.
Find 26th term.
In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.
The 26th, 11th and the last term of an A.P. are 0, 3 and -1/5, respectively. Find the common difference and the number of terms.
If the nth term of the A.P. 9, 7, 5, …. is same as the nth term of the A.P. 15, 12, 9, … find n.
3, 5, 7, 9, …. 201
3,8,13, … ,253
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1.
Find the first term and the common difference.
Find the second term and the nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
How many numbers of two digit are divisible by 3?
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34.
Find the first term and the common difference of the A.P.
The first term of an A.P. is 5 and its 100th term is -292.
Find the 50th term of this A.P.
Find a30 – a20 for the A.P.
-9, -14, -19, -24
a, a+d, a+2d, a+3d, ……
Write the expression an – ak for the A.P. a, a+d, a+2d, …..
Hence, find the common difference of the A.P. for which
11th term is 5 and 13th term is 79.
a10 – a5 = 200
20th term is 10 more than the 18th term.
Find n if the given value of x is the nth term of the given A.P.
25, 50, 75, 100, ; x = 1000
-1, -3, -5, -7, …; x = -151
5½, 11, 16½, 22, ….; x = 550
1, 21/11, 31/11, 41/11, …; x = 171/11
The eighth term of an A.P is half of its second term and the eleventh term exceeds one third of its fourth term by 1.
Find the 15th term.
Find the arithmetic progression whose third term is 16 and the seventh term exceeds its fifth term by 12.
The 7th term of an A.P. is 32 and its 13th term is 62.
Find the A.P.
Which term of the A.P. 3, 10, 17, …. will be 84 more than its 13th term ?
Two arithmetic progressions have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Which term of the AP 3, 8, 13, …. is 248?
If x + 1, 3x and 4x + 2 are in A.P., find the value of x.
Find the value of x for which (8x + 4), (6x – 2) and (2x + 7) are in A.P.
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Show that (a – b)², (a² + b²) and (a + b)² are in A.P.
Find the sum of the following arithmetic progressions:
3, 9/2, 6, 15/2, … to 25 terms
50, 46, 42, … to 10 terms
1, 3, 5, 7, … to 12 terms
– 26, – 24, – 22, …. to 36 terms
41, 36, 31, … to 12 terms
a + b, a – b, a – 3b, … to 22 terms
(x – y)2, (x2 + y2), (x + y)2, to 22 tams
\frac{x-y}{x+y}, \frac{3 x-2 y}{x+y}, \frac{5 x-3 y}{x+y} \text {, to } n \text { terms }
Find the sum of last ten terms of the A.P. : 8, 10, 12, 14, .. , 126
Find the sum to n terms of the A.P. 5, 2, –1, – 4, –7, …
Find the sum of n terms of an A.P. whose the terms is given by an = 5 – 6n.
Find the sum of all 3 – digit natural numbers which are divisible by 13.
Find the sum of first 15 terms of each of the following sequences having nth term as:
an = 3 + 4n
bn = 5 + 2n
xn = 6 – n
yn = 9 – 5n
Find the sum of first 20 terms the sequence whose nth term is an = An + B.
Find the sum of first 25 terms of an A.P whose nth term is given by an = 2 – 3n.
Find the sum of first 25 terms of an A.P whose nth term is given by an = 7 – 3n.
If the sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19, . . ., is 116.
Find the last term.
Find the sum:
2 + 4 + 6 + . . . + 200
How many terms of the sequence 18, 16, 14…. should be taken so that their sum is zero.
How many terms are there in the A.P. whose first and fifth terms are -14 and 2 respectively and the sum of the terms is 40?
How many terms of the A.P. 9, 17, 25, . . . must be taken so that their sum is 636?
Find the sum of all 3 – digit natural numbers which are multiples of 11.
How many terms of the A.P. 63, 60, 57, . . . must be taken so that their sum is 693?
1 + 3 + 5 + 7 + . . . + 199
How many terms of the A.P. is 27, 24, 21. . . should be taken that their sum is zero?
Find the sum of the first
11 terms of the A.P. : 2, 6, 10, 14, . . .
13 terms of the A.P. : -6, 0, 6, 12, . . .
51 terms of the A.P. : whose second term is 2 and fourth term is 8.
Find the sum of the first 15 multiples of 8.
Find the sum of the first 40 positive integers divisible by 3 .
Find the sum of the first 40 positive integers divisible by 5.
3 + 11 + 19 + . . . + 803
Find the sum of the first 40 positive integers divisible by 6.
(-5) + (-8) + (-11) + . . . + (- 230)
7+10 \frac{1}{2}+14+\cdots+84
34 + 32 + 30 + . . . + 10
25 + 28 + 31 + . . . + 100
The first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2.
Find the first term, the common difference and the sum of first 20 terms.
The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442.
Find the common difference.
If 12th term of an A.P. is -13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
Find the sum of n terms of the series
\left(4-\frac{1}{n}\right)+\left(4-\frac{2}{n}\right)+\left(4-\frac{3}{n}\right)+\ldots .
In an A.P., if the first term is 22, the common difference is – 4 and the sum to n terms is 64, find n.
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
Find the sum of first 51 terms of an A.P. whose second and third terms are 14 and 18 respectively.
If the sum of 7 terms of an A.P. is 49 and that of 17 terms is 289, find the sum of n terms.
The sum of first seven terms of an A.P. is 182. If its 4th and 17th terms are in ratio 1: 5, find the A.P.
The nth term of an A.P is given by (-4n + 15).
Find the sum of first 20 terms of this A.P.
In an A.P. the sum of first ten terms is -150 and the sum of its next 10 term is -550.
Sum of the first 14 terms of an A.P. is 1505 and its first term is 10.
Find its 25th term.
In an A.P. , the first term is 2, the last term is 29 and the sum of the terms is 155.
Find the common difference of the A.P.
The first and the last term of an A.P are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Find the number of terms of the A.P. –12, –9, –6, . . . , 21. If 1 is added to each term of this A.P., then find the sum of all terms of the A.P. thus obtained.
The first term of an A.P. is 5, the last term is 45 and the sum is 400.
Find the number of terms and the common difference.
In an A.P. the first term is 22, nth term is -11 and the sum of first n term is 66.
Find n and the d, the common difference.
The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find the common difference.
The first and the last terms of an A.P are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.
The sum of first q terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1: 2. Find the first and 15th term of the A.P.
If the 10th term of an A.P. is 21 and the sum of its first 10 terms is 120, find its nth term.
The sum of first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161.
Find the 28th term of this A.P.
In an A.P. the first term is 8, nth term is 33 and the sum of first n term is 123.