Let S_k denote the sum of first k terms of an AP. What is S_ 30 S_ 20 -S_ 10 equal to?

Correct answer: C. 3 Let first term be ' a ' and common differenced be ' d ' of an A.P. aligned & s_ 30 s_ 20 -s_ 10 =((30)/(2)[2 a+29 d])/((20)/(2)[2 a+19 d]-(10)/(2)[2 a+9 d]) & =(15[2 a+29 d])/(20 a+190 d-10 a-45 d) & =(15(2 a+29 d))/(10 a+145 d)=(15(2 a+29 d))/(5(2 a+29 d))=3 aligned

NDA 2021

Exam: NDA
Year: 2021
Subject: Mathematics
Chapter: Sequences and Series

NDA 2021 · Mathematics · Sequences and Series

Let S_k denote the sum of first k terms of an AP. What is S_ 30 S_...

Let

S_k

denote the sum of first

k

terms of an AP. What is

\frac{S_{30}}{S_{20}-S_{10}}

equal to?

Options

Correct answer

C. 3

Step-by-step solution

Let first term be '

a

' and common differenced be '

d

' of an A.P.

\begin{aligned} & \therefore \frac{s_{30}}{s_{20}-s_{10}}=\frac{\frac{30}{2}[2 a+29 d]}{\frac{20}{2}[2 a+19 d]-\frac{10}{2}[2 a+9 d]} \\ & \quad=\frac{15[2 a+29 d]}{20 a+190 d-10 a-45 d} \\ & =\frac{15(2 a+29 d)}{10 a+145 d}=\frac{15(2 a+29 d)}{5(2 a+29 d)}=3\end{aligned}

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