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?
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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.
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