Question

The number of terms of the ap 5,8,11.... To betp taken so that the sum is 258

Answer 1

Answer:

12 terms

Step-by-step explanation:

the AP is 5, 8, 11 ......

a = 5 d = 3 Sn = 258

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

$258 = \frac{n}{2} (2(5) + (n - 1)3) \\ 258 = \frac{n}{2} (10 + 3n - 3) \\ 258 \times 2 = n(7 + 3n) \\ 516 = 7n + 3 {n}^{2} \\ 3 {n}^{2} + 7n - 516 = 0 \\ 3 {n}^{2} - 36n + 43n - 516 = 0 \\ 3n(n - 12) + 43(n - 12) = 0 \\ (n - 12)(3n + 43) = 0 \\ n - 12 = 0 \: \: \: \: 3n + 43 = 0 \\ n = 12 \: \: \: \: \: n = - \frac{43}{3}$

as the number of terms cannot be negative or in fraction

we take the positive value of n = 12

therefore the number of terms to be taken to get sum of 258 is 12

verification

$= \frac{12}{2} (2(5) + (12 - 1)3) \\ = 6(10 + 33) \\ = 6 \times 43 \\ = 258$

hope you get your answer