Question

Find the 64th term of the arithmetic sequence

Answer 1

Answer:

The 64th term of the arithmetic sequence is -1075.

Step-by-step explanation:

Arithmetic sequence:

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

The nth term of an arithmetic sequence is given by:

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

In which $a_1$ is the first term.

−4,−21,−38

First term -4, so $a_1 = -4$

Common difference of $d = -38 - (-21) = -21 - (-4) = -17$

Thus

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

$a_n = -4 - 17(n-1)$

Find the 64th term of the arithmetic sequence

This is $a_{64}$. So

$a_n = -4 - 17(n-1)$

$a_{64} = -4 - 17(64-1) = -4 - 1071 = -1075$

The 64th term of the arithmetic sequence is -1075.