Question

how many terms are to be added to make the sum 52 in the series {-8}+{-6}+{-4}+​

Answer 1

Answer:

let n be the number of terms ,

n/2×(-16+2n-2)=52

n(n-9)=52

n=13

Answer 2

Step-by-step explanation:

the AP is -8, -6, -4 ...........

a = -8, d = 2

Sn = n/2 (2a + (n-1)d)

$52 = \frac{n}{2} (2( - 8) + (n - 1)2) \\ 52 = \frac{n}{2} ( - 16 + 2n - 2) \\ 52 = \frac{n}{2} (2n - 18) \\ 52 = \frac{n}{2} \times 2(n - 9) \\ 52 = {n}^{2} - 9n \\ {n}^{2} - 9n - 52 = 0 \\ {n}^{2} - 13n + 4n - 52 = 0 \\ n(n - 13) + 4(n - 13) = 0 \\ (n - 13)(n + 4) = 0 \\ n - 13 = 0 \: \: \: \: \: n + 4 = 0 \\ n = 13 \: \: \: \: \: \: n = - 4$

we take the positive value of x = 13

sum of 13 terms will be 52

$s13 = \frac{13}{2} (2( - 8) + (13 - 1)2) \\ = \frac{13}{2} ( - 16 + 24) \\ = \frac{13}{2} \times 8 \\ = 13 \times 4 \\ = 52$

hope you get your answer