Question

Consider the arithmetic sequence presented in the table below.


n 3 64
an 126 3,725


Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference.

Part A: What is the first term, a1, of the sequence?

Part B: What is the general term equation, an, for this sequence?

Part C: What is the value of the 13th term of this sequence?

Answer 1

So you've got the formula \(a_n = a_1 + (n − 1)d\) and we have 2 'n's and 2 '\(a_n\)'s. From this, you can make a system of equation
\(126 = a_1 + (3 − 1)d...(1)\)
\(3725 = a_1 + (64 − 1)d...(2)\)

Answer 2

Now you should be able to find \(a_1\) and d by substitution or elimination method, whichever method you prefer.