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Insertion of AP's between 2 Numbers

100 A.Ms are ...

Question

100 A.Ms are inserted between 20 and 80. Find the sum of first A.M and last A.M

A

100

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B

80

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C

60

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D

92

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Solution

The correct option is A
100

Let the common difference be d. Then the A.P will be
$20, 20 + d - ----- -, 20 + 2 d . . . . . .80 - 2 d, 80 - d - ----- -, 80$
$\Rightarrow$ Sum of first and last A.M (underlined terms)
$\Rightarrow 20 + d + 80 - d = 100$

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A. M.s are inserted between

20

80

such that first mean: last mean =

1 : 3

.Find the value of

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