Question

Find the 90th term of the arithmetic sequence 16 , 21 , 26

Answer 1

Answer:

The 90th term of the arithmetic sequence is 461.

Step-by-step explanation:

Arithmetic sequences concepts:

The general rule of an arithmetic sequence is the following:

$a_{n+1} = a_{n} + d$

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

$a_{n} = a_{1} + (n-1)*d$

In this question:

$a_{1} = 16, d = 21 - 16 = 26 - 21 = 5$

So

90th term

$a_{90} = a_{1} + (90-1)*d$

$a_{90} = 16 + 89*5$

$a_{90} = 461$

The 90th term of the arithmetic sequence is 461.