Question

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

Answer 1

a₁₅₇ = 1,088

Explanation:

aₙ = a₁ + d(n-1); where 'd' if common difference

a₁₅₇ = -4 + 7(156)

= -4 + 1092

= 1,088

Answer 2

157 is the 24th term

Explanation:

The formula for arithmetic sequences is an=a1+(n-1)d,

where an is the nth term, a1 is the first term, n is the term position, and d is the common difference

First, we need to find the common difference using the 10.

Since it's the third term, we have 10=-4+(3-1)d

Solving for d gives us d=7

Next, we need to find the term number of 157

Thus, we have 157=-4+(n-1)*7

Solving for n gives us n=24

We can check it like this: Following order of operations (i.e. PEMDAS) gives us 24-1=23*7=161-4=157