math precalculus 12

Question

If an Arithmetic series has a first term of a = 4 and t₃ = 8, the determine S_10.

Answer 1

The nth partial sum of an arithmetic sequence is determined by S_n = (n/2)[2a₁ + (n-1)d] where a₁ is the first term, and d is the common difference between terms. From this we simply plug in the values.

n = 15

a1 = 4

d = ?

Since the 3rd term is 8 and the difference between terms is constant, we can deduce that d = 8-4/2 = 2.

So we have S₁₅ = (15/2)[2(4) + (14)(2)] = 270.