Question

The common difference of an arithmetic sequence is 1 and the product of the first and the third terms is 143. What are the first three terms?

Answer 1

Common difference of an arithmetic sequence = 1

Let the second term be x.

∴ First term = x − 1

Third term = x + 1

Product of the first term and the third term = 143

⇒ (x − 1)(x + 1) = 143

If x = 12, then the second term = 12

First term = x − 1 = 12 − 1 = 11

Third term = x + 1 = 12 + 1 = 13

If x = −12, then the second term = −12

First term = x − 1 = −12 − 1 = −13

Third term = x + 1 = −12 + 1 = −11

Therefore, the first three terms of the sequence are 11, 12, and 13 or −13, −12, and −11.