Let a1, a2, a3, .

Question

Let a1, a2, a3, . . . . . . . , an, . . . . . be in A.P.

If a3 + a7 + a11 + a15 = 72,

then the sum of its first 17 terms is equal to :

Accepted Answer

As  a1 a2 . . . . . an . . . . . are in A.P.

$$ \therefore $$   a3 + a15 = a7 + a11 = a1 + a17

Given,

a3 + a7 + a11 + a15 + a15 = 72

$$ \Rightarrow $$   (a3 + a15) + (a7 + a11) = 72

$$ \Rightarrow $$   2(a1 + a17) = 72

$$ \Rightarrow $$   (a1 + a17) = 36

$$ \therefore $$   Sum of first 17 terms

= $${{17} \over 2}$$ (a1 + a17)

= $${{17} \over 2}$$ $$ \times $$ 36

= 306

Solutions · 1