Answer:

PROBLEM

Which of the following is the common difference of an arithmetic sequence whose a2 = 1, a5 = 7?

ANSWER

The common difference is 2

SOLUTION

Since we don't have a 1st term and we need one,

Let's make a2 be the a1, hence a2 = a1

then a5 would be a4, thus, a5 = a4

We get a4 by subtracting the number of terms that we also subtract from a2 to be a1, which is only 1.

The given will be,

an = last term = 7

a1 = first term = 1

n = number of terms = 4

Getting the common difference,

\begin{gathered}a_{n} = a_{1} + (n - 1)(d) \\ 7 = 1 + (4 - 1)(d) \\ 7 = 1 + 3(d) \\ 7 - 1 = 3d \\ 6 = 3d \\ \frac{6}{3} = d \\ 2 = d\end{gathered}an=a1+(n−1)(d)7=1+(4−1)(d)7=1+3(d)7−1=3d6=3d36=d2=d