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If there are 3 A.M's between 4 and 84, find their sum.

Question

If there are $3 A . M^{'} s$ between $4$ and $84$ , find their sum.

88

132

166

336

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Benjamin Discussed

If there are

3 A . M^{'} s

between

4

and

84

, find their sum.

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Let the 3 AMs be

A_{1}, A_{2}, A_{3}

then

4, A_{1}, A_{2}, A_{3}, 84

forms an arithmetic progression

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

here,

n = 5, a = 4, a_{n} = 84 S_{n} = \frac{5}{2} (4 + 84) = 220

220 = 4 + A_{1} + A_{2} + A_{3} + 84 A_{1} + A_{2} + A_{3} = 220 - 88 A_{1} + A_{2} + A_{3} = 132

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Question Text	If there are $3 A . M^{'} s$ between $4$ and $84$ , find their sum.
Answer Type	Text solution:1
Upvotes	150