Question

In the arithmetic sequence -7, -4, -1, 2, ..., what term is 26

Answer 1

Hi,

12th term.

Explanation:

The given sequence is an arithmetic sequence with a common difference of 3.

We can find the term using the formula for the nth term of an arithmetic sequence:

`a_n=a_1+(n-1)*d\\`

where:

`a_n` is the nth term of the sequence

`a_1` is the first term

d is the common difference between the terms

n is the term number we want to find

Here, we have:

`a_1=-7\ (first\ term)\\d=3\ (common\ difference)\\`

We want to find the term where
`a_n=26`.

Let's substitute these values into the formula and solve for n:

`26=-7+(n-1)*3\\`

`Simplify\ this\ equation:\\26=-7+3*n-3\\26=3*n-10\\\\Add\ 10\ to\ both\ sides:36=3*nDivide\ both\ sides\ by\ 3:n=12\\`

So, the 12th term of the sequence is 26.