Question

Given the Arithmetic sequence A 1 , A 2 , A 3 , A 4 32, 42, 52, 62 What is the value of A16 ?

Answer 1

a16 = 148

Explanation:

There are other ways to do this, but the simplest way to get to a1 is just to subtract two terms you know to get d.

a6 - a5 = 42 - 32 = 10

so a4 = a6 - a5 = 42 - 32 = 10

a4 = 32 - 10 = 22 [a5 - 10]

a3 = 22 - 10 = 12 [a4 - 10]

a2 = 12 - 10 = 2 [a3 - 10]

a1 = 2 - 10 = - 8 [a2 - 10]

Givens

a1 = - 8

d = 10

Term number = n = 16

Formula

an = a1 + (n - 1)*d

Solution

n = 16

a1 = - 2

d = 10

a16 = -2 + (16 - 1) * 10

a16 = -2 + 15*10

a16 = -2 + 150

a16 = 148