Question

Write an equation for the nth term of the arithmetic sequence. Then find a40.

Answer 1

Answer:

The nth term is: $a_n = \frac{1}{4} + \frac{1}{4}(n-1)$

a40 = 10

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.

The nth term of a sequence is given by:

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

In which $a_1$ is the first term and d is the common difference.

1/4,1/2

This means that:

$d = \frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}$

1/4

This means that $a_1 = \frac{1}{4}$

The nth term is:

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

$a_n = \frac{1}{4} + \frac{1}{4}(n-1)$

Then find a40.

$a_{40} = \frac{1}{4} + \frac{1}{4}(40-1) = \frac{1}{4} + \frac{39}{4} = \frac{40}{4} = 10$

So

a40 = 10