Question

The 5^th term of an arithmetic sequence is 11 and its 12^th term is 32. What are its first three terms?

Answer 1

5^th term of the arithmetic sequence = 11

12^th term of the arithmetic sequence = 32

To get the 12^th term from the 5^th term, we must add the common difference seven times to the 5^th term.

The number to be added is 32 − 11 = 21

∴ Common difference = = 3

We can get the 5^th term from the 1^st term by adding the common difference four times to the 1^st term.

So, in this sequence, the 5^th term, i.e., 11 is received by adding 4 × 3 = 12 to the 1^st term.

∴ 1^st term = 11 − 12 = −1

Now, the 1^st term is −1 and the common difference is 3.

∴2^nd term = −1 + 3 = 2

3^rd term = 2 + 3 = 5

So, the first three terms of the given arithmetic sequence are −1, 2 and 5.