Question

28th term of -1,-5,-9,-13

Answer 1

The 28th term of sequence is -109

Solution:

Given sequence is:

-1, -5, -9, -13

Let us first find the difference between the terms

-5 - (-1) = -5 + 1 = -4

-9 - (-5) = -9 + 5 = -4

-13 - (-9) = -13 + 9 = -4

Thus the difference between the terms remains constant

This is a arithmetic sequence

The nth term of arithmetic sequence is given by formula:

$a_n = a_1 + (n-1)d$

Where,

$a_n$ is the nth term of sequence

$a_1$ is the first term of sequence

d is the common difference between terms

Here, -1, -5, -9, -13

First term = $a_1$ = -1

d = -4

Substituting the values in formula,

$a_n = -1+(n-1)(-4)\\\\a_n = -1 -4n + 4\\\\a_n = -4n + 3$

To find 28th term, substitute n = 28

$a_{28} = - 4 \times 28+3\\\\a_{28} =-112+3\\\\a_{28} =-109$

Thus the 28th term of sequence is -109