Question

The first term of an arithmetic sequence is -3 and the fifteenth term is 53.

What is the common difference of the sequence?

Answer 1

The \(n^{th}\) term of an arithmetic sequence is: \(a_n = a_1 + (n-1)d\) where \(a_1\) is the first term and \(d\) is the common difference.
Here, \(a_1 = -3;~~n = 15;~~a_{15} = 53\). Plug in and find d.

Answer 2

where does a15 go?

Answer 3

The left hand side. when n = 15, \(\large a_n \text{ becomes } a_{15}\)

Answer 4

\[\large
a_n = a_1 + (n-1)d \\ \large
a_1 = -3;~~n = 15;~~a_{15} = 53 \\ \large
53 = -3 + (15 - 1)d \\ \large
53 + 3 = 14d \\ \large
56 = 14d \\ \large
d = 56/14 = 4
\]

Answer 5

Thanks!!

Answer 6

You are welcome.