Question

how many terms of the AP 24,21,18.... must be taken so that their sum is 78?​

Answer 1

Answer:

n=4 and 13

Step-by-step explanation:

Using formula

$Sn = \frac{n}{2} (2a1 + (n - 1)d) \\ 78 = \frac{n}{2} (2 \times 24 + (n - 1) \times - 3) \\ 78 \times 2 = 48n + ({n}^{2} - n) \times - 3 \\ 156 = 48n - 3 {n}^{2} + 3n \\ 156 = - 3 {n}^{2} + 51n \\ 3 {n}^{2} - 51n + 156 = 0 \\ 3 {n}^{2} - 39n - 12n + 156 = 0 \\ 3n(n - 13) - 12(n - 13) = 0 \\ (3n - 12)(n - 13) = 0$

Hence,

n = 13

And n = 4