Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...

The 13th term is 81x + 59.

Step-by-step explanation:

We are given the arithmetic sequence:

And we want to find the 13th term.

Recall that for an arithmetic sequence, each subsequent term only differ by a common difference d. In other words:

Find the common difference by subtracting the first term from the second:

Distribute:

Combine like terms. Hence:

The common difference is (7x + 5).

To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

Where a is the initial term and d is the common difference.

The initial term is (-3x - 1) and the common difference is (7x + 5). Hence:

To find the 13th term, let n = 13. Hence:

Simplify:

The 13th term is 81x + 59.

d

step-by-step explanation:

the solution is in the picture