Question

The 5^th term of an arithmetic sequence is 9 and its 9^th term is 5. What is its common difference? What is the 14^th term?

Answer 1

5^th term of the arithmetic sequence = 9

9^th term of the arithmetic sequence = 5

To get the 9^th term from the 5^th term, we must add the common difference four times to the 5^th term.

The number to be added is 5 − 9 = −4

∴ Common difference = = −1

To get the 14^th term from the 5^th term, we must add the common difference nine times to the 5^th term.

∴ 14^th term = 9 + 9(−1) = 9 − 9 = 0