ARITHMETIC SERIES PRACTICE WORKSHEET

Question 1 :

Find the sum of the following APs

(i)  2 , 7 , 12,....... to 10 terms            Solution

(ii) -37, -33, -29,..................... to 12 terms           Solution

(iii) 0.6, 1.7, 2.8,............... to 100 terms           Solution

(iv) 1/15, 1/12, 1/10,................... to 11 terms           Solution

Question 2 :

Find the sums given below

7 + 10   1/2 + 14 + ...............+ 84

Solution

Question 3 :

In an arithmetic series a₁ = 7 and a₁₂ = 29. Find the sum of first 12 terms.

Solution

Question 4 :

In an arithmetic series the first term is 8 the common difference is 1/2 and the sum of the first n terms is 220.5. Find the value of n.

Solution

Question 5 :

How many terms of the arithmetic series 25 + 19 + 13 + ........ are required to give a sum of -20 ?

Solution

Question 6 :

The first 3 terms of an arithmetic progression are 1, 4, 7. Find the 47th term and the sum of first 47 terms.

Solution

Question 7 :

Find the sum of first 31 terms of the sequence 15, 13, 11, .......

Solution

Question 1 :

 Find the sums given below

7 + 10 (1/2) + 14 + ...............+ 84     Solution

Question 2 :

34 + 32 + 30 + .................. + 10     Solution

Question 3 :

- 5 + (-8) + (-11) + .............+ (-230)    Solution

Question 4 :

150 workers were engaed to finish a piece of work in certain number of days. Four workers dropped the second day, four more workers dropped the third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed.

Solution

Question 5 :

How many terms of the AP -15,-13,-11,… are needed to make the sum -55?

Solution

Question 6 :

Solve the equation : (−4) + (−1) + 2 +⋯+ 𝑥 = 437

Solution

Question 7 :

The sum of the first 7 terms of an AP is 63 and that of its next 7 terms is 161. Find the AP.

Solution

Question 1 :

Find the sum of first 22 terms of an AP in which d = 7 and 22^nd term is 149. 

Solution

Question 2 :

The sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Solution

Question 3 :

The 15th term of the AP 13, 17, 21, 25,… is

(a) 102     (b) 104      (c) 69      (d) 108

Solution

Question 4 :

The sum of first 16th terms of the AP 10, 6, 2, ….is

Solution

Question 5 :

The sum of first three terms of an AP is 33. If the product of first and third term exceeds the second term by 29, find the AP

Solution

Question 6 :

In an AP, if 𝑎 = 1, 𝑎_𝑛 = 20, 𝑆_𝑛 = 399 then n is equal to

a) 19    b) 21    c) 38      d) 42

Solution

Question 7 :

If the 𝑛𝑡ℎ term of an AP is given by 𝑎_𝑛 = 5𝑛 − 3 then the sum of first 10 terms if

a) 225    b) 245   c) 255  d) 270

Solution

Question 1 :

If the sum of 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms. 

Solution

Question 2 :

Show that a₁, a₂,............ an form an AP where an is defined as below

(i) a_n  =  3 + 4n

(ii) a_n  =  9 - 5n

Also find the sum of 15 terms in each case.

Solution

Question 3 :

A partial sum of an arithmetic sequence is given. Find the sum 

3 + 7 + 11 + ............. + 39

Solution

Question 4 :

A partial sum of an arithmetic sequence is given. Find the sum 

Solution

Question 5 :

A partial sum of an arithmetic sequence is given. Find the sum 

Solution

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