Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Sequences and Series

NDA 2024 · Mathematics · Sequences and Series

The mean of n observations 1,4,9,16, , n^2 is 130. What is the...

The mean of nn observations 1,4,9,16,…,n21,4,9,16, \ldots, n^2 is 130. What is the value of nn ?

Options

  1. A18
  2. B19
  3. C20
  4. D21

Correct answer

B. 19

Step-by-step solution

 Mean =1+4+9+……+n2n130=n(n+1)(2n+1)6n⇒780n=n(n+1)(2n+1)⇒780=2n2+3n+1⇒2n2+3n−779=0⇒(2n+41)(n−19)=0⇒x=−412,19⇒n=19(∵n=−412 not possible )\begin{aligned} & \text{ Mean }=\frac{1+4+9+\ldots \ldots+\mathrm{n}^2}{\mathrm{n}} \\ & 130=\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{6 \mathrm{n}} \\ & \Rightarrow 780 \mathrm{n}=\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1) \\ & \Rightarrow 780=2 \mathrm{n}^2+3 \mathrm{n}+1 \\ & \Rightarrow 2 \mathrm{n}^2+3 \mathrm{n}-779=0 \\ & \Rightarrow(2 \mathrm{n}+41)(\mathrm{n}-19)=0 \\ & \Rightarrow \mathrm{x}=-\frac{41}{2}, 19 \\ & \Rightarrow \mathrm{n}=19 \quad\left(\because \mathrm{n}=-\frac{41}{2} \text{ not possible }\right)\end{aligned}$$
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