Question

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

Answer 1

157 is the 24th term.

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:

`\displaystyle x_n=a+d(n-1)`

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:

`x_n= -4 + d(n-1)`

Since 10 is the third term, n = 3:

`\displaystyle x_(3)=10=-4+d(3-1)`

Solve for the common difference:

`14=2d\Rightarrow d=7`

Hence, our direct formula is:

`\displaystyle x_n=-4+7(n-1)`

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

`\displaystyle (157)=-4+7(n-1)`

Therefore:

`\displaystyle \begin{aligned} 161 &= 7(n-1) \\ 23 & = n-1 \\ n &= 24\end{aligned}`

157 is the 24th term.