Subject - Mathematics:

Arithmetic Progression

MCQ - 446-9178

Question:

The 5th term of an AP is – 3 and its common difference is – 4. The sum of its first 10 terms is

50
– 50
30
– 50

Correct Answer: B

Explanation:

Let a be the first term and d be the common difference.
Given: a₅ = - 3
Common difference = d = - 4
Now, Consider a₅ = - 3
⇒ a + 4d = - 3
⇒ a + 4(-4) = - 3
⇒ a - 16 = - 3
⇒ a = 16 - 3
⇒ a = 13
Now, Sum of first n terms of an AP is
S_n = $\frac{n}{2}$ [2a + (n - 1)d]
∴ Sum of first 10 terms is given by:
S₁₀ = $\frac{10}{2}$ [2(13) + (10 - 1)(-4)]
= 5[26 - 36]
= 5 × (-10)
= - 50

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