In a certain armithmetic sequence , if -4 is the first term , and 10 is the third term, which term is 157?

157 is the 24th term.

Step-by-step explanation:

We are given that in an arithmetic sequence, -4 is the first term and 10 is the third term. And we want to find the term number of 157.

Recall that the direct formula for an arithmetic sequence is given by:

Where n is the nth term, a is the initial term, and d is the common difference.

We know that the initial term a is -4. Hence:

Since 10 is the third term, n = 3:

Solve for the common difference:

Hence, our direct formula is:

To find the term number of 157, let 157 equal xₙ and solve for n. Hence:

Therefore:

157 is the 24th term.