Mathematics exemplar problems class 10 Solutions for Chapter 5 arithmetic progressions

Exercises in Chapter 5 arithmetic progressions Grade 10

Arithmetic Progressions - Exercise 5.1

Arithmetic Progressions - Exercise 5.2

Arithmetic Progressions - Exercise 5.3

Arithmetic Progressions - Exercise 5.4

Questions in Arithmetic Progressions - Exercise 5.1

The list of numbers – 10, – 6, – 2, 2,… is

In an AP, if d = –4, n = 7, a_n = 4, then a is

In an AP, if a = 3.5, d = 0, n = 101, then a_n will be

The first four terms of an AP, whose first term is –2 and the common difference is –2, are

The 21st term of the AP whose first two terms are –3 and 4 is

If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7^th term?

Which term of the AP: 21, 42, 63, 84… is 210?

If the common difference of an AP is 5, then what is a₁₈ – a₁₃?

What is the common difference of an A.P. in which a₁₈ – a₁₄ = 32 ?

In an A.P., if a = 1, a_n = 20 and S_n = 399 then n is

Two APs have the same common difference. The 1st term of one of these is –1 and that of other is –8. Then the difference between their 4th terms is

If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then its 18th term will be

The 4^th term from the end of the A.P. –11, –8, –5, …, 49 is

If the first term of an A.P. is –5 and the common difference is 2, then the sum of first 6 terms is

The sum of first 16 terms of the A.P. 10, 6, 2, … is

The sum of first five multiples of 3 is

The 11th term of the AP: –5, (–5/2), 0, 5/2, …is

Questions in Arithmetic Progressions - Exercise 5.2

The number of bacteria in a certain food item after each second, when they double in every second. Do the lists of numbers involved form an A.P.?

Justify whether it is true to say that –1, -3/2, –2, 5/2,… forms an AP as a₂ – a₁ = a₃ – a₂.

The taxi fare after each km, when the fare is Rs 15 for the first km and Rs 8 for each

additional km, does not form an A.P., as the total fare (in Rs) after each km is 15, 8, 8, 8,

… Is the statement true

Is –1, –1, –1, –1,… an A.P. ?

Is 0, 2, 0, 2,… an A.P. ?

Is 11, 22, 33… an A.P. ?

Is 1/2,1/3,1/4, … an A.P. ?

Is √3, √12, √27, √48, … an A.P. ?

Is 2, 2², 2³, 2⁴, … an A.P. ?

Justify whether it is true for the AP: –3, –7, –11, …, can we find directly a₃₀ – a₂₀ without actually finding a₃₀ and a₂₀?

Justify whether it is true to say that 2n – 3 are the n^th terms of an A.P.

Is 0 a term of the A.P. 31, 28, 25, … ?

The fee charged from a student every month by a school for the whole session, when

the monthly fee is Rs 400. Do the lists of numbers involved form an A.P.?

The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of 10% per annum. Do the lists of numbers involved form an A.P.?

Justify whether it is true to say that 3n² + 5 is the nth term of an A.P

Justify whether it is true that 1 + n + n² is the nth term of an A.P.

Two A.P.s have the same common difference. The first term of one A.P. is 2, and that of the other is 7. The difference between their 10^th terms is same as the difference between their 21^st terms, which is the same as the difference between any two corresponding terms.

Is 1, 1, 2, 2, 3, 3… an A.P. ?

The fee charged every month by a school from classes I to XII, when the monthly fee for class I is Rs 250, and it increase by Rs 50 for the next higher class. Do the lists of numbers involved form an A.P.?

Questions in Arithmetic Progressions - Exercise 5.3

Write the next three terms of 0, 1/4, 1/2, 3/4,…

The first term of an A.P. is –5 and last term is 45. If the sum of the terms of the A.P. is 120, then find the number of terms and the common difference.

Check whether 5, 14/3, 13/3, 4… is an A.P.

Write the next three terms of 5, 14/3, 13/3, 4…

Check whether √3 , 2√3, 3√3,… is an A.P.

Write the next three terms of √3 , 2√3, 3√3,…

Check whether a + b, (a + 1) + b, (a + 1) + (b + 1), … is an A.P.

Check whether a, 2a + 1, 3a + 2, 4a + 3,… is an A.P.

Write the next three terms of a, 2a + 1, 3a + 2, 4a + 3,…

Which term of the A.P., –2, –7, –12, … will be –77 ?

Find the sum of the A.P. –2, –7, –12, … upto the term –77.

If a_n = 3 – 4n, that a₁, a₂, a_3, … from an A.P. Find S₂₀.

In an A.P., if S_n = n(4n + 1) then find the A.P.

In an A.P. if S_n = 3n² + 5n and a_k = 164, then find the value of k.

Find the sum of first 17 terms of an A.P. whose 4th and 9th terms are –15, and –30 respectively.

If sum of first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sun of the first 10 terms.

Find the sum of all the 11 terms of an A.P. whose middle most term is 30

Find the sum of last 10 terms of the A.P. 8, 10, 12, ..., 126.

Find the sum of 1 + (–2) + (–5) + (–8) + … + (–236)

Find the sum of $\left(4-\frac{1}{n}\right)+\left(4-\frac{2}{n}\right)+\left(4-\frac{3}{4}\right)+\ldots\text{ up to }\mathrm{n}\text{ terms }$ .

Find the sum of $\frac{a-b}{a+b}+\frac{3a-2b}{a+b}+\frac{5a-3b}{a+b}+\ldots\text{ up to }11\text{ terms }$

Write the next three terms of a + b, (a + 1) + b, (a + 1) + (b + 1), …

Check whether 0, 1/4, 1/2, 3/4,… is an A.P. ?

Find the sum of first seven numbers which are multiples of 2 as well as of 9.

How many terms of the A.P.: –15, –13, –11, … are needed to make the sum –55 ?

The sum of first n terms of an A.P. whose first terms is 8 and the common difference is 20 is equal to the sum of first 2n terms of another A.P. whose first term is –30, and the common difference is 8. Find n.

Kanika was given her pocket money on Jan. 1, 2008. She puts ₹ 1 on day 1, ₹ 2 on day 2, ₹ 3 on day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent ₹ 204 of her pocket money, and found that at the end of the month she still had ₹ 100 with her. How much was her pocket money for the month ?

Yasmeen saves ₹ 32 during the first month, ₹ 36 in the second month and ₹ 40 in 3rd month. if she continues to save in this manner, in how many months will she save ₹ 2000 ?

Find 55 is which term of the A.P.: 7, 10, 13, …

If the 9th term of an A.P. is zero, find the term that is twice its 19th term.

Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.

Find a, b and c such that the following numbers are in AP: a, 7, b, 23, c.

Fidn the first three terms of the AP when a = –5, d = –3.

Find the first three terms of the AP when a =1/2, d = -1/6.

Find the first three terms of the AP when a = √2 , d = 1/√2.

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.

The sum of the 5th and the 7th term of an A.P is 52 and the 10th term is 46. Find the A.P.

Find the 20th term of an A.P. whose 7th term is 24 less than the 11th term, first term being 12.

Split 207 into three parts such that these are in A.P. and the product of the two smaller parts is 4623. Find the A.P.

Find the 12th term from the end of the A.P.: –2, –4, –6, …, –100.

If nth terms of two A.P.s: 9, 7, 5, … and 24, 21, 18, … are same, then find the values of n Also find that term.

Which term of the A.P.: 53, 48, 43, … is the first negative term ?

If the sum of 3rd and the 8^th terms of an A.P. is 7 and the sum of 7th and 14th terms is –3, find the 10th term.

How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3 ?

Find the sum of the two middle most terms of an A.P. $\frac{-4}{3},-1,\frac{-2}{3},\ldots4\frac{1}{3}$

Find the common difference of a₂ = 13, a₄ = 3.

Find the common difference of A.P. : 2, –2, –6, –10, …

Find the common difference of a = 0, a₁₀ = 6.

If S_n denotes the sum of first n terms of an A.P., such that S₁₂ = n/2(S₈ – S₄). Find n.

Find the common difference of a = –18, n = 10, a_n = 0.

Questions in Arithmetic Progressions - Exercise 5.4

The ratio of the 11th term to the 18th term of an A.P. is 2 : 3. Find the ratio of the 5th

term to the 21st term and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

Solve the equation – 4 + (–1) + 2 + … + x = 437

Jaspal Singh repays his total loan of ₹ 118000 by paying every month starting with the first instalment of ₹ 1000. If he increases the instalment by ₹ 100 every month, what amount will be paid by him in the 30th instalment ? What amount of loan does he still have to pay after the 30th instalment ?

The sum of the sum of first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.

The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1. Find the 15th term.

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.

Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.

Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5 .

Find the sum of the integers between 100 and 200 that is not divisible by 9.

Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.

Find the sum of the integers between 100 and 200 that is divisible by 9.

**The sum of an A.P. whose first term is a, the second term b and the last

term c, is **