R d sharma solutions mathematics class 10 Solutions for Chapter 8 arithmetic progressions

Exercises in Chapter 8 arithmetic progressions Grade 10

Arithmetic Progressions Exercise 9.1

Arithmetic Progressions Exercise 9.2

Arithmetic Progressions Exercise 9.3

Arithmetic Progressions Exercise 9.4

Arithmetic Progressions Exercise 9.5

Arithmetic Progressions Exercise 9.6

Questions in Arithmetic Progressions Exercise 9.1

Write the first terms of each of the following sequences whose n^th term are:

a_n = 3n + 2

Write the first terms of each of the following sequences whose nth term are:

a_n = (n – 2)/3

Write the first terms of each of the following sequences whose nth term are:

a_n = 3ⁿ

Write the first terms of each of the following sequences whose nth term are:

$a_{n}=\frac{3 n-2}{5}$

Write the first terms of each of the following sequences whose nth term are:

a_n = (-1)ⁿ2ⁿ

Write the first terms of each of the following sequences whose nth term are:

a_n = 2n² – 3n + 1

Write the first terms of each of the following sequences whose nth term are:

a_n = n(n – 2)/2

Write the first terms of each of the following sequences whose nth term are:

a_n = (2n – 3)/ 6

Write the first terms of each of the following sequences whose nth term are:

a_n = n² – n + 1

Questions in Arithmetic Progressions Exercise 9.2

Show that the sequence defined by a_n = 5n – 7 is an A.P., find its common difference.

Show that the sequence defined by a_n = 3n² – 5 is not an A.P.

The general term of a sequence is given by a_n = -4n + 15. Is the sequence an A.P.? If so, find its 15^th term and the common difference.

Questions in Arithmetic Progressions Exercise 9.3

For the following arithmetic progressions write the first term a and the common difference d:

– 5, -1, 3, 7,…

For the following arithmetic progressions write the first term a and the common difference d:

1/5, 3/5, 5/5, 7/5,…

For the following arithmetic progressions write the first term a and the common difference d:

0.3, 0.55, 0.80, 1.05,…

For the following arithmetic progressions write the first term a and the common difference d:

-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

Write the arithmetic progression when first term a and common difference d are as follows:

a = –1, d = 1/2

Write the arithmetic progression when first term a and common difference d are as follows:

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.

In which of the following situations, the sequence of numbers formed will form an A.P.?

The amount of air present in the cylinder when a vacuum pump removes each time 1/4 of their remaining in the cylinder.

In which of the following situations, the sequence of numbers formed will form an A.P.?

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.

Questions in Arithmetic Progressions Exercise 9.4

Find:

10^th term of the AP 1, 4, 7, 10….

Find:

18^th term of the AP √2, 3√2, 5√2, …….

Find:

n^th term of the AP 13, 8, 3, -2, ……….

Find:

10^th term of the AP -40, -15, 10, 35, ………….

Find:

8^th term of the AP 11, 104, 91, 78, ……………

Find:

11^th term of the AP 10.0, 10.5, 11.0, 11.2, …………..

Find:

9^th term of the AP 3/4, 5/4, 7/4 + 9/4, ………..

Find the 12^th 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

How many terms are there in the A.P.?

-1, -5/6, -2/3, -1/2, … , 10/3

How many terms are there in the A.P.?

7, 13, 19, …, 205

How many terms are there in the A.P.?

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 6^th and 17^th terms of an A.P. are 19 and 41 respectively, find the 40^th term.

If 9^th term of an A.P. is zero, prove its 29^th term is double the 19^th term.

If 10 times the 10^th term of an A.P. is equal to 15 times the 15^th term, show that 25^th term of the A.P. is zero.

The 10^th and 18^th terms of an A.P. are 41 and 73 respectively.

Find 26^th term.

In a certain A.P. the 24^th term is twice the 10^th term. Prove that the 72^nd term is twice the 34^th term.

The 26^th, 11^th 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 n^th term of the A.P. 9, 7, 5, …. is same as the n^th term of the A.P. 15, 12, 9, … find n.

Find the 12^th term from the end of the following arithmetic progressions:

3, 5, 7, 9, …. 201

Find the 12^th term from the end of the following arithmetic progressions:

3,8,13, … ,253

The 4^th term of an A.P. is three times the first and the 7^th term exceeds twice the third term by 1.

Find the first term and the common difference.

Find the second term and the n^th term of an A.P. whose 6^th term is 12 and the 8^th 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 32^nd term.

The sum of 4^th and 8^th terms of an A.P. is 24 and the sum of the 6^th and 10^th 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 100^th term is -292.

Find the 50^th term of this A.P.

Find a₃₀ – a₂₀ for the A.P.

-9, -14, -19, -24

Find a₃₀ – a₂₀ for the A.P.

a, a+d, a+2d, a+3d, ……

Write the expression a_n – a_k for the A.P. a, a+d, a+2d, …..

Hence, find the common difference of the A.P. for which

11^th term is 5 and 13^th term is 79.

Write the expression a_n – a_k for the A.P. a, a+d, a+2d, …..

Hence, find the common difference of the A.P. for which

a₁₀ – a₅ = 200

Write the expression a_n – a_k for the A.P. a, a+d, a+2d, …..

Hence, find the common difference of the A.P. for which

20^th term is 10 more than the 18^th term.

Find n if the given value of x is the n^th term of the given A.P.

25, 50, 75, 100, ; x = 1000

Find n if the given value of x is the n^th term of the given A.P.

-1, -3, -5, -7, …; x = -151

Find n if the given value of x is the n^th term of the given A.P.

5½, 11, 16½, 22, ….; x = 550

Find n if the given value of x is the n^th term of the given A.P.

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 15^th term.

Find the arithmetic progression whose third term is 16 and the seventh term exceeds its fifth term by 12.

The 7^th term of an A.P. is 32 and its 13^th term is 62.

Find the A.P.

Which term of the A.P. 3, 10, 17, …. will be 84 more than its 13^th term ?

Two arithmetic progressions have the same common difference. The difference between their 100^th terms is 100, what is the difference between their 1000^th terms?

Which term of the AP 3, 8, 13, …. is 248?

Questions in Arithmetic Progressions Exercise 9.5

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.

Questions in Arithmetic Progressions Exercise 9.6