Question

The sum of first 16 terms of the AP: 10, 6, 2,... is
(A) –320 (B) 320 (C) –352 (D) –400

NCERT Class X
Mathematics - Exemplar Problems

Chapter _ARITHMETIC PROGRESSIONS

Answer 1

the formula for the sum of first n terms of a AP is n/2(2a+(n-1)d)
here n=16 a=10 d=6-10=2-6=-4
so sum of first 16 terms=16/2(2·10+(16-1)·-4)
=8(20+15·-4)
=8(20-60)
=8(-40)
=-320
therefore the option is A

Answer 2

Answer:

a)-320

Step-by-step explanation:

Given,

First term, a = 10

Common Difference, d = 6 - 10 = - 4 (a2 - a1)

Using the formula,

Where $s_{n}$ is the sum of first n terms, n = no of terms, a = first term, d = common difference

$s_{n}$=(n/2)[2a+(n-1)d]

$s_{16}$ = (16/2)[ 2(10) + (16 - 1) (- 4)]

= 8(20 - 60)

= - 320

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