Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Sequences and Series

NDA 2015 · Mathematics · Sequences and Series

What is the sum of n terms of the series 2 + 8 + 18 + 32 + . ?

What is the sum of n terms of the series \sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+\ldots. ?

Options

  1. An(n−1)2\frac{\mathrm{n}(\mathrm{n}-1)}{\sqrt{2}}
  2. B2n(n+1)\sqrt{2 \mathrm{n}}(\mathrm{n}+1)
  3. Cn(n+1)2\frac{\mathrm{n}(\mathrm{n}+1)}{\sqrt{2}}
  4. Dn(n−1)2\frac{\mathrm{n}(\mathrm{n}-1)}{2}

Correct answer

C. n(n+1)2\frac{\mathrm{n}(\mathrm{n}+1)}{\sqrt{2}}

Step-by-step solution

2+8+18+32+….=2+22+32+42+…..∴Sn=2[1+2+3+4+….n terms ]=2n(n+1)2=n(n+1)2\begin{aligned} & \sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+\ldots. \\ & =\sqrt{2}+2 \sqrt{2}+3 \sqrt{2}+4 \sqrt{2}+\ldots.. \\ & \therefore \mathrm{S}_{\mathrm{n}}=\sqrt{2}[1+2+3+4+\ldots. \mathrm{n} \text{ terms }] \\ & =\sqrt{2} \frac{\mathrm{n}(\mathrm{n}+1)}{2}=\frac{\mathrm{n}(\mathrm{n}+1)}{\sqrt{2}}\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