Question

The sum of 6th and 10th terms of an arithmetic sequence is 66.
What is the sum of first and 15th terms of this sequence?

Answer 1

Arithmetic Sequence

Given: the sum of the 6th and the 10th terms is 66

To find: the sum of the 1st and the 15th terms

Solution:

• Let the 1st term be a and the common difference be d

• Then, 6th term = a + 5d,
• 10th term = a + 9d and
• 15th term = a + 14d

• Given, 6th term + 10th term = 66
• or, a + 5d + a + 9d = 66
• or, 2a + 14d = 66 ....(1)

• Sum of the 1st and the 15th terms is
• = a + a + 14d
• = 2a + 14d
• = 66 [ by (1)]

Answer: the sum of the 1st and the 15th terms is 66.