One of the most important and exam oriented question from Chapter name- Arithmetic Progression

Class 10th

Chapter number- 9

Exercise :- 9.6

This type of question has been asked in previous years exams.

In this question we have been given that the sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161

Now we have to find the 28th term of this A.P.

CBSE DHANPAT RAI publication

CBSE Mathematics Class 10th

Question 30

Sum of first 7 terms of an A.P., S

_{7}Â = 63.And sum of next 7 terms is 161.

So, the sum of first 14 terms, S

_{14}Â = Sum of first 7 terms + Sum of next 7 termsS

_{14}Â = 63 + 161 = 224By using the formula of the sum of n terms of an A.P.

S

_{n}Â = n[2a + (n âˆ’ 1)d] / 2.So, S

_{7}Â = 7(2a + (7 âˆ’ 1)d) / 2=> 7(2a + 6d) / 2 = 63

=> 2a + 6d = 18 . . . . (1)

Also, S

_{14}Â = 14(2a + (14 âˆ’ 1)d) / 2=> 14(2a+13d)/2 = 224

=> 2a+13d = 32 Â . . . . (2)

Now, subtracting eq(1) from eq(2), we get

=> 13d â€“ 6d = 32 â€“ 18

=> 7d = 14

=> d = 2

On putting d = 2 in eq(1), we get,

=> 2a + 6(2) = 18

=> 2a = 18 â€“ 12

=> a = 3

Thus, a

_{28}Â = a + (28 â€“ 1)d = 3 + 27 (2) = 3 + 54 = 57Hence, the 28th term is 57.This is the video solution for this question. Thank you!!