Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Sequences and Series

NDA 2019 · Mathematics · Sequences and Series

What is the n^ th term of the sequence 25,-125,625 , -3125, ?

What is the nth \mathrm{n}^{\text{th }} term of the sequence 25,−125,62525,-125,625, −3125,…-3125, \ldots ?

Options

  1. A(−5)2n−1(-5)^{2 \mathrm{n}-1}
  2. B(−1)2n5n+1(-1)^{2 \mathrm{n}} 5^{\mathrm{n}+1}
  3. C(−1)2n−15n+1(-1)^{2 \mathrm{n}-1} 5^{\mathrm{n}+1}
  4. D(−1)n−15n+1(-1)^{\mathrm{n}-1} 5^{\mathrm{n}+1}

Correct answer

D. (−1)n−15n+1(-1)^{\mathrm{n}-1} 5^{\mathrm{n}+1}

Step-by-step solution

Given series 25,−125,625,−3125……25,-125,625,-3125 \ldots \ldots is geometric progression. a=t1=25,t2=−125r=t2t1=−12525=−5\mathrmnthterm⁡(tn)=arn−1=(25)(−5)n−1=(5)2(−1)n−1(5)n−1=(−1)n−1(5)2+n−1=(−1)n−15n+1\begin{aligned} & \mathrm{a}=\mathrm{t}_1=25, \mathrm{t}_2=-125 \\ & r=\frac{t_2}{t_1}=\frac{-125}{25}=-5 \\ & \mathrmn^{\mathrm{th}} \operatorname{term}\left(\mathrm{t}_{\mathrm{n}}\right)=\mathrm{ar}^{\mathrm{n}-1} \\ & =(25)(-5)^{\mathrm{n}-1} \\ & =(5)^2(-1)^{\mathrm{n}-1}(5)^{\mathrm{n}-1} \\ & =(-1)^{\mathrm{n}-1}(5)^{2+\mathrm{n}-1} \\ & =(-1)^{\mathrm{n}-1} 5^{\mathrm{n}+1}\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