UPSC NDA Math Model Paper 1

Let the first term be 'a' and common difference be 'd'
Given: the sum of first 10 terms and 20 terms of an AP are 120 and 440
Now,
S10=120
⇒

10

2

[2a+(10−1)×d]=120
⇒5[2a+9d]=120
⇒2a+9d=24 .......(1)
S20=440
⇒

20

2

[2a+(20−1)×d]=440
⇒10[2a+19d]=440
⇒2a+19d=44 .... (2)
Subtraction equation (2) from (1), we get
(2a + 19d) - (2a + 9d) = 44 - 24
⇒ 10d = 20
∴ d = 2
Put the value of d in equation (1), we get
⇒ 2a + 9 × 2 = 24
⇒ 2a = 6
∴ a = 3