3. What is the first term of the arithmetic sequence whose 8^{th} and 26^{th} 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 (a_{1} – d). So, since a_{8} = 20 and a_{26} = 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,