$a_{1}, a_{2}, a_{3} . . . . . . ., a_{15} a r e i n A . P a n d a_{1} + a_{8} + a_{15} = 15 t h e n a_{2} + a_{3} + a_{8} + a_{13} + a_{14}$ is equal to:

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Solution

$\frac{a_{1} + a_{15}}{2} = a_{8}$ $a_{1}, a_{2}, a_{3}, . . . \dots, a_{8}, a_{14}, a_{15}$
$a_{1} + a_{8} + a_{15} = 15$ $\frac{a_{1} + a_{15}}{2} = \frac{a_{2} + a_{14}}{2}$
$\Rightarrow 3 a_{8} = 15$ $= \frac{a_{3} + a_{13}}{2} = a_{8}$
$\Rightarrow a_{8} = 5$
$a_{2} + a_{3} + a_{8} + a_{13} + a_{14}$
$(a_{2} + a_{14}) + (a_{3} + a_{13}) + a_{8} = 2 a_{8} + 2 a_{8} + a_{8}$
$= 5 a_{8} = 5 (5)$
$= 25$ .

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