Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Sequences and Series

NDA 2023 · Mathematics · Sequences and Series

In an AP, the first term is x and the sum of the first n terms is...

In an AP, the first term is xx and the sum of the first nn terms is zero. What is the sum of next mm terms?

Options

  1. Amx(m+n)n−1\frac{m x(m+n)}{n-1}
  2. Bmx(m+n)1−n\frac{m x(m+n)}{1-n}
  3. Cnx(m+n)m−1\frac{n x(m+n)}{m-1}
  4. Dnx(m+n)1−m\frac{n x(m+n)}{1-m}

Correct answer

B. mx(m+n)1−n\frac{m x(m+n)}{1-n}

Step-by-step solution

a=xSn=0n2[2a+(n−1)d]=02a+(n−1)d=0(∵n≠0)a=xS n=0\frac{n}{2}[2 a+(n-1) d]=02 a+(n-1) d=0(\because \mathrm{n} \neq 0) Sum of next mm terms = Sum of (m+n)(m+n) terms - (Sum of first nn - terms) Sm+n=m+n2[2a+(m+n−1)d]−0=m+n2[2x−2x(m+n−1)n−1]=(m+n)x[1−m+n−]=(m+n)x[<u>n−1−m−n+1</u>]=−m(m+n)xn−1=m(m+n)x1−nS_{m+n}=\frac{m+n}{2}[2 a+(m+n-1) d]-0=\frac{m+n}{2}\left[2 x-\frac{2 x(m+n-1)}{n-1}\right]=(m+n) x\left[1-\frac{m+n-}{}\right]=(m+n) x[<u>n-1-m-n+1</u>]=\frac{-m(m+n) x}{n-1}=\frac{m(m+n) x}{1-n}.
Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Let p , q and r be three unequal numbers such that p , q and r are in AP. If (q-p)… NDA 2026If p^ th term of an AP is k , then what is the sum of p^ th term, (p+q)^ th term and… NDA 2026If p , g_1 , g_2 and q are in GP and m is the arithmetic mean of p and q , then… NDA 2026The sum of the first n terms of an AP is 3n^2+5n . If the m^ th term of the AP is 68… NDA 2026Passage: Let X(a,p) , Y(b,q) and Z(c,r) be the points such that a , b and c are in AP.… NDA 2026If (10 + _ 10 x) , (10 + _ 10 y) and (10 + _ 10 z) are in AP, then consider the following… NDA 2025How many terms of the series 1 + 3 + 5 + 7 + … amount to a sum equal to 12345678987654321… NDA 2025For the following two (02) items: Let (6 + 10 + 14 + … up to m terms) = (1 + 3 + 5 + 7 +… NDA 2025For the following two (02) items: Let (6 + 10 + 14 + … up to m terms) = (1 + 3 + 5 + 7 +… NDA 2025How many terms are identical in the two APs 19, 21, 23, … up to 110 terms and 19, 22, 25… NDA 2025If p , 1 , q are in AP and p , 2 , q are in GP, then which of the following statements… NDA 2025The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If r ≠ 1… NDA 2025If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term… NDA 2025The sum of the first k terms of a series S is 3k^2 + 5k . Which one of the following is… NDA 2025What is the harmonic mean of the numbers C(10,3) , C(10,4) , C(10,5) , C(10,6) and… NDA 2025If p times the p^ th term of an AP is equal to q times the q^ th term (p ≠ q) , then what… NDA 2024 Full Sequences and Series list Sequences and Series JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs