Question

How many terms of sequence -8 -6 -4,..... must be taken so that their sum is 70

Answer 1

Answer:

14 terms

Step-by-step explanation:

a = -8 ,

d = -6 - (-8) = -6+8 = +2

given Sₙ = 70

we have to find n.

we know Sₙ = (n/2) [2a+(n-1)d]

(n/2) [2a+(n-1)d] = 70 (given)

substitute value of 'a' & 'd'

(n/2) [2(-8)+(n-1)2] = 70

n *  [-16+2n-2] = 70 *2 = 140

-18n+2n² = 140

n²-9n-70 = 0

solving the quadratic eqn , we get

(n-14)(n+5) = 0

so n = 14 or n = -5

omit the negative value of n (as no. of terms cannot be negative)

=> the no. of terms to make the sum of the a.p to be 70 is 14