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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Sequences and Series

NDA 2023 · Mathematics · Sequences and Series

Let a_1, a_2, a_3 be in AP such that a_1+a_5+a_ 10 +a_ 15 +a_ 20...

Let a1,a2,a3…a_1, a_2, a_3 \ldots be in AP such that a1+a5+a10+a15+a20+a25+a30+a34=300a_1+a_5+a_{10}+a_{15}+a_{20}+a_{25}+a_{30}+a_{34}=300 What is a1+a5−a10−a15−a20−a25+a30+a34a_1+a_5-a_{10}-a_{15}-a_{20}-a_{25}+a_{30}+a_{34} equal to?

Options

  1. A0
  2. B25
  3. C125
  4. D250

Correct answer

A. 0

Step-by-step solution

Since, a1+a5−a10−a15−a22−a25+a30+a34=a1+a1+4d−a1−9d−a1−14d−a1−19d=a1−24d+a1+29d+a1+33d=0\begin{aligned} & a_1+a_5-a_{10}-a_{15}-a_{22}-a_{25}+a_{30}+a_{34} \\ & =a_1+a_1+4 d-a_1-9 d-a_1-14 d-a_1-19 d \\ & =a_1-24 d+a_1+29 d+a_1+33 d \\ & =0 \end{aligned}
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