Maths / Arithmetic Progression / Sum of First n Terms

QUESTION

If the sum of first 9 terms of an AP is equal to the sum of first 13 terms, the sum of first 22 terms will be _______

 OPTIONS A. 0 B. 1 C. -1 D. 35
Right Option : A

EXPLANATION
Explain TypeExplanation Content
Text

$\dpi{80} \LARGE S_9=S_1_3$

I.E.,$\dpi{80} \LARGE \frac{9}{2}[2a+(9-1)d]=\frac{13}{2}[2a+13-1)d]$

$\dpi{80} \LARGE \Rightarrow$ 18a+72d=26a+156d

i.e.,8a=-84d

i.e.,2a=-21d

Now,$\dpi{80} \LARGE S_2_2=\frac{22}{2}[2a+(22-1)d]=11(2a+11d)$

=11(2a-2a)=0

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