Question

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

Answer 1

Answer:

n = 4 or n = 13

Step-by-step explanation:

24, 21, 18.........

a = 24 d = -3

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

78 = n/2 (2(24) + (n-1)(-3))

$78 = \frac{n}{2} (2(24) + (n - 1)( - 3)) \\ 78 \times 2 = n(48 - 3n + 3) \\ 156 = n(51 - 3n) \\ 156 = 51n - 3 {n}^{2} \\ 3 {n}^{2} - 51n + 156 = 0 \\ 3( {n}^{2} - 17n + 52) = 0 \\ {n}^{2} - 17n + 52 = 0 \\ {n}^{2} - 13n - 4n + 52 = 0 \\ n(n - 13) - 4(n - 13) = 0 \\ (n - 13)(n - 4) = 0 \\ n - 13 = 0 \: \: \: \: \: \: \: n - 4 = 0 \\ n = 13 \: \: \: \: \: \: \: n = 4$

therefore the sum of 4 terms or 13 terms will be equal to 78

as the AP has negative numbers in the series

hope you get your answer