a term in an arithmetic sequence is 488. the first term of the sequence is 7 and the common difference is 13. find the term number.

Answer: the term number is 38

Step-by-step explanation:

Let the number of the term be x

The value of the xth term = 488

In an arithmetic sequence, the terms differ by a common difference, d. This means that the difference between two consecutive terms, d is constant.

The formula for the nth term is

Tn = a + (n-1) d

Where

Tn = the nth term of the arithmetic sequence

a = the first term of the arithmetic sequence.

d = common difference.

From the information given,

a = 7

d = 13

We are looking for the xth term.

Tx = 488 = 7 + (x-1) 13

488 = 7 + 13x - 13

Collecting like terms on the left hand side and right hand side of the equation,

13x = 488 - 7 + 13

13x = 494

x = 38

The value of the 38th term is 488.