MCQ - 450-9182

Correct Answer: B

Explanation:

Let a be the first term and d be the common difference.
Given: a₁₃ = 4(a₃)
a₅ = 16
To find: Sum of first ten terms.
Now, Consider a₁₃ = 4a₃
⇒ a + 12d = 4[a + 2d]
⇒ a + 12d = 4a + 8d
⇒ 3a = 4d ………. (1)
Consider a₅ = a + (5 - 1)d = 16
⇒ a + 4d = 16
⇒ a + 3a = 16 (from equation (1))
⇒ 4a = 16
⇒ a = 4 ………. (2)
∴ d = 3
Sum of n terms of an arithmetic series is given by:
S_n =$\genfrac{}{}{1px}{}{\mathrm{n}}{2}$ [2a + (n - 1)d]
Therefore sum of 10 terms of the arithmetic series is given by:
∴ S₁₀ = $\genfrac{}{}{1px}{}{10}{2}$ [2(4) + (10 - 1)(3)]
= 5 × [8 + 27]
= 5 × 35
= 175