QJEEM25Ma01f3: JEE Main 2025 Mathematics - Class 11 JEEM25Ma01f3 Solution: In an arithmetic progression, if and , then is equal to :

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QJEEM25Ma01f3: JEE Main 2025 Mathematics - Class 11 JEEM25Ma01f3 Solution: In an arithmetic progression, if and , then is equal to :

In an arithmetic progression, if $\mathrm{S}_{40}=1030$ and $\mathrm{S}_{12}=57$ , then $\mathrm{S}_{30}-\mathrm{S}_{10}$ is equal to :

Multiple Choice Options

A 525
B 505
C 510
D 515

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Accepted Answer

Let a & d are first term and common diff of an AP.

$\begin{aligned} S_{40} = \frac{40}{2} [2 a + 39 d] = 1030 ..... (1) \\ S_{12} = \frac{12}{2} [2 a + 11 d] = 57 ..... (2) \end{aligned}$

by (1) & (2)

$\begin{aligned} a = - \frac{7}{2} d = \frac{3}{2} \\ ∴ S_{30} - S_{10} = \frac{30}{2} [2 a + 29 d] - \frac{10}{2} [2 a + 9 d] \\ = 20 a - 390 d \\ = 515 \end{aligned}$

QJEEM25Ma01f3: JEE Main 2025 Mathematics - Class 11 JEEM25Ma01f3 Solution: In an arithmetic progression, if and , then is equal to :

Multiple Choice Options

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