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What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is - 14 and the 6th term is - 5?

What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is - 14 and the 6th term is - 5? Correct Answer -42

CONCEPT:

In this question we need to recall the formulas used in arithmetic progression

FORMULAE USED:

an = a + (n - 1)d

Sum of first 12 numbers = (n / 2)(a + a12)

SOLUTION:

3rd term is - 14

6th term is - 5

-14 = a + 2d   ---(1)

-5 = a + 5d   ---(2)

Solving (1) and (2) simultaneously

a = -20

d = 3

⇒ Sum of first 12 numbers = 6 (-20 + 13) = 6 × (-7)

∴ Sum of first 12 numbers = -42

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