Question

For an arithmetic series it is known that the first term is 2, the common difference is 5, and the sum is 87. Determine the number of terms in this series

Answer 1

Step-by-step explanation:

a = 2

d= 5

Sn = 87

n/2 × { 2a +(n-1)d } =87

n/2 ×{2×2+(n-1)5} = 87

n/2×{4+5n-5} = 87

n/2× 5n - 1 = 87

5n^2 - n / 2 = 87

5n^2 -n = 87×2

5n^2 -n = 174

5n^2 - n - 174 =0

5n^2 -30n +29n -174 =0

5n(n -6) +29(n - 6 )= 0

(n - 6) (5n-29) = 0

n = 6 or n = 29/5

Since , n cannot be in fraction , n = 6