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The sum of the fourth and twelfth term of an arithmetic progre

Question

The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

A

150

B

200

C

250

D

500

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The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

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Text solutionVerified

Here we use the formula for the nth term and sum of A.P:

a_{n} = a + (n - 1) d

&

S_{n} = \frac{n}{2} (2 a + (n - 1) d)

∴

a_{4} + a_{12} = 20

\Rightarrow a + 3 d + a + 11 d = 20

\Rightarrow 2 a + 14 d = 20

Now

S_{15} = \frac{15}{2} (2 a + 14 d) = \frac{15 \times 20}{2} = 150

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Question Text	The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?
Answer Type	Text solution:1
Upvotes	152