3. What is the first term of the arithmetic sequence whose 8th and 26th terms are 20 and 56 respectively?

 

A. 1

B. 2

C. 6

D. 8

E. 9

 

Solution: The answer is C

Since the nth term of an arithmetic sequence is given by,

Where d is, by definition, the common difference between any two consecutive terms of the sequence and c is defined as (a1 d). So, since a8 = 20 and a26 = 56, we have the following two equations:

To solve for d, subtract equation 2 from equation 1. As follows,

To solve for c, substitute d into any of the two above equations, say equation 2. As follows,

Thus, the first term of this arithmetic sequence is given by,