Question

in arithmetic progression 7, 10, 13, ... how
mamy terms will add up to a sum of 920?
5 b) 16 (c) 27 (d 3​

Answer 1

Step-by-step explanation:

a = 7

10 - 7 = 13 - 10

3 = 3

d = 3

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

$920 = \frac{n}{2} (2(7) + (n - 1)3) \\ 920 = \frac{n}{2} (14 + 3n - 3) \\ 920 \times 2 = n(3n + 11) \\ 1840 = 3 {n}^{2} + 11n \\ 3 {n}^{2} + 11n - 1840 = 0 \\ 3 {n}^{2} - 69n + 80n - 1840 = 0 \\ 3n(n - 23) + 80(n - 23) = 0 \\ (n - 23)(n + 80) = 0 \\ n - 23 = 0 \: \: \: n + 80 = 0 \\ n = 23 \: \: \: \: \: \: \: \: \: \: \: \: n = - 80$

number of terms cannot be negative

therefore number of terms is 23

hope you get your answer