Question

Determine the number of terms, n, in the arithmetic series a₁=16, aₙ=96 and Sₙ = 616

(only type in the number)

Answer 1

The number of terms in the given arithmetic series is 11, which is determined by using the sum formula for an arithmetic series and solving for n.

Step-by-step explanation:

To determine the number of terms, n, in the arithmetic series with the first term a₁ = 16, the nth term aₙ = 96, and the sum of the first n terms Sₙ = 616, we can use the formulas for the arithmetic series. The sum of an arithmetic series is given by Sₙ = n/2 * (a₁ + aₙ). By substituting the given values into this formula, we can solve for n.

616 = n/2 * (16 + 96)
616 = n/2 * 112
n = 616 * 2 / 112
n = 11

Therefore, the number of terms in the series is 11.