Question

how many terms of the ap 24,21,18,.... must be terms so that there sum is 38 ​

Answer 1

Answer:

n = 4, n = 13

Step-by-step explanation:

We don't get 38 as sum of terms in the given AP

The sum should be 78 not 38

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

the AP is 24, 21, 18 .......

a = 24

d = -3

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

we get n = 4 and n = 13

sum of 4 terms and sum of 13 terms gives us 78

hope you get your answer