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For an AP, the sum of the first 6 terms equals the sum of the first 10 terms. What is $S_{16}$ ?

Class 10Properties and Selection of AP TermsAlgebra — Sequences

AIt cannot be found
B16
C1
D0

Step-by-Step Solution

3 (2 a + 5 d) = 5 (2 a + 9 d)

gives

6 a + 15 d = 10 a + 45 d

, so

2 a = - 15 d

, i.e.

2 a + 15 d = 0. S_{16} = 8 (2 a + 15 d) = 0

.

Answer: D) 0

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