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After inserting n A.M.'s between 2 and 38, the sum of the resu

Question

After inserting n A.M.'s between $2$ and $38$ , the sum of the resulting progressions is $200$ . The value of n is?

7

8

9

10

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Benjamin Discussed

After inserting n A.M.'s between

2

and

38

, the sum of the resulting progressions is

200

. The value of n is?

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

If there are

N

arithmetic and if there are

N

arithmetic means between

2

and

38

, then there are

N + 2

terms

And the first term is

2

and the last term is

38

We know that,

S_{n} = \frac{n}{2} (a + ℓ)

Here,

n = N + 2, a = 2, ℓ = 38

and

S_{N + 2} = 200

∴ S_{N + 2} = \frac{N + 2}{2} (2 + 38)

\Rightarrow 200 = \frac{N + 2}{2} (2 + 38)

400 = 40 (N + 2)

\Rightarrow 10 = (N + 2)

N = 8

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Question Text	After inserting n A.M.'s between $2$ and $38$ , the sum of the resulting progressions is $200$ . The value of n is?
Answer Type	Text solution:1
Upvotes	150