Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesA.P.Easy2 minPYQ_2020

MathematicsEasystatement

If the first term of an $A . P .$ is $3$ and the sum of its first $25$ terms is equal to the sum of its next $15$ terms, then the common difference of this $A . P .$ is

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Answer:

Solution:

Sum of first $25$ terms=sum of next $15$ terms

$S_{25} = S_{N e x t 15}$

$\Rightarrow S_{25} + S_{N e x t 15} = S_{40}$

$\Rightarrow 2 \times S_{25} = S_{40}$

$\Rightarrow 2 \times \frac{25}{2} [2 \times 3 + 24 d] = \frac{40}{2} [2 \times 3 + 39 d]$

$\Rightarrow 5 [2 \times 3 + 24 d] = 4 [2 \times 3 + 39 d]$

$\Rightarrow 30 + 120 d = 24 + 156 d$

$\Rightarrow 36 d = 6 \Rightarrow d = \frac{1}{6}$

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:A.P.

⏱ 2mℹ️ Source: PYQ_2020

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