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Properties of AP

If a1, a2, ...

Question

If $a_{1}, a_{2}, a_{3}, . . . . . . . ., a_{25}$ are in A.P and $a_{3} + a_{5} + a_{12} + a_{14} + a_{21} + a_{23} = 60$ , then $a_{2} + a_{7} + a_{19} + a_{24} =$

A

30

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B

40

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C

120

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D

180

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Solution

The correct option is B $40$
$a_{1}, a_{2}, a_{3}, . . . . . . a_{25}$ are in AP.

$a_{3}, a_{5}, a_{12} + a_{14} + a_{21} + a_{23} = 60$

$\Rightarrow a + 2 d + a + 4 d + a + 11 d + a + 13 d + a + 20 d + a + 22 d = 60$

$\Rightarrow 6 a + 72 d = 60$

$\Rightarrow a + 12 d = 10$

Consider $a_{2} + a_{7} + a_{19} + a_{24} = a + d + a + 6 d + a + 18 d + a + 23 d$

$= 4 a + 48 d$

$= 4 (a + 12 d)$

$= 4 (10) = 40$ .

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