# The Nth Term of an Ap is Given by (−4n + 15). Find the Sum of First 20 Terms of this Ap. - Mathematics

Sum

The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?

#### Solution

Given, an = − 4n + 15

∴ a1 = − 4 × 1 + 15 = − 4 + 15 = 11

a2 = − 4 × 2 + 15 = − 8 + 15 = 7

a3 = − 4 × 3 + 15 = − 12 + 15 = 3

a4 = − 4 × 4 + 15 = − 16 + 15 = −1

It can be observed that

a2 − a1 = 7 − 11 = −4

a3 − a2 = 3 − 7 = −4

a4 − a3 = − 1 − 3 = −4

i.e., ak + 1 − ak is same every time. Therefore, this is an A.P. with common difference as

−4 and first term as 11.

S_n=n/2[2a+(n-1)d]

S_20=20/2[2(11)+(20-1)(-4)]

=10[22+19(-4)]

=10(20-76)

=10(-54)

=-540

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 32 | Page 52