How do you write the first five terms of the arithmetic sequence given a_8=26, a_12=42?

1 Answer
Aug 8, 2018

-2, 2, 6, 10, 14

Explanation:

The general term of an arithmetic sequence is given by the formula:

a_n = a + d(n-1)

where a is the initial term and d the common difference.

Given a_8 = 26 and a_12 = 42, we find:

16 = 42-26

color(white)(16) = a_12 - a_8

color(white)(16) = (a+11d) - (a+7d)

color(white)(16) = 4d

Hence d=4

Then:

26 = a_8 = a+7d = a+28

Hence a=-2

So the first five terms of the sequence are:

-2, 2, 6, 10, 14