Find the second and third term of the arithmetic sequence -7, __, __, -22, -27

Solution:

A progression is a sequence of numbers that follow a specific pattern.

An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same.

Given, the arithmetic sequence is -7, __, ___, -22, -27,...

We have to find the second and third terms of the arithmetic sequence.

The n^th term of the arithmetic sequence is given by a_n=a+(n-1)d

Here, first term, a = -7

Common difference, d = -27 - (-22)

d = -27 + 22

d = -5

So, \(a_{2}=-7+(2-1)(-5)\\a_{2}= -7-5\\a_{2}=-12\)

\(a_{3}=-7+(3-1)(-5)\\a_{3}= -7-(2)5\\a_{3}=-7-10\\a_{3}=-17\)

Therefore, the second and third terms are -12 and -17.

Find the second and third term of the arithmetic sequence -7, __, __, -22, -27

Summary:

The second and third terms of the arithmetic sequence -7, __, __, -22, -27 is -12 and -17.