First slide

Arithmetic progression

Question

If $a_{1}, a_{2}, a_{3}$ is an $A . P .$ such that $a_{1} + a_{5} + a_{10} + a_{15} + a_{20} + a_{24} = 225$ then $a_{1} + a_{2} + a_{3} + \dots \dots + a_{23} + a_{24}$ is equal to

Moderate

A

909
B

75
C

750
D

900

Solution

We have,
$\begin{array}{l} a_{1} + a_{5} + a_{10} + a_{15} + a_{20} + a_{24} = 225 \\ \Rightarrow (a_{1} + a_{24}) + (a_{5} + a_{20}) + (a_{10} + a_{15}) = 225 \\ \Rightarrow 3 (a_{1} + a_{24}) = 225 \Rightarrow a_{1} + a_{24} = 75 \\ ∴ a_{1} + a_{2} + a_{3} + \dots \dots + a_{24} = \frac{24}{2} (a_{1} + a_{24}) = 12 \times 75 = 900 \end{array}$

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