Let t_1, t_2, t_3, be in GP. What is (t_1 t_3 t_ 21 )^ (1)/(11) equal to?

Correct answer: C. t_ 11 since, t_1, t_2, t_3 in G.P Let t_n=a r^ n-1 Now, (t_1. t_3 .. t_ 21 )^ (1)/(11) aligned & =( ^ 11 ^ 110 )^ (1)/(11) =ar^ 10 =t_ 11 aligned

NDA 2023

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

NDA 2023 · Mathematics · Sequences and Series

Let t_1, t_2, t_3, be in GP. What is (t_1 t_3 t_ 21 )^ (1)/(11)...

Let

t_1, t_2, t_3, \ldots

be in GP. What is

\left(t_1 t_3 \ldots t_{21}\right)^{\frac{1}{11}}

equal to?

Options

A $t_{10}$
B $t_{10}^2$
C $t_{11}$
D $t_{11}^2$

Correct answer

C. $t_{11}$

Step-by-step solution

since,

t_1, t_2, t_3 \ldots \ldots

in G.P Let

\quad t_n=a r^{n-1}

Now,

\quad\left(t_1. t_3 \ldots.. t_{21}\right)^{\frac{1}{11}}

\begin{aligned} & =\left(\mathrma^{11} \mathrmr^{110}\right)^{\frac{1}{11}}=\mathrm{ar}^{10}=\mathrm{t}_{11} \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 2026 If p^ th term of an AP is k , then what is the sum of p^ th term, (p+q)^ th term and… NDA 2026 If p , g_1 , g_2 and q are in GP and m is the arithmetic mean of p and q , then… NDA 2026 The sum of the first n terms of an AP is 3n^2+5n . If the m^ th term of the AP is 68… NDA 2026 Passage: Let X(a,p) , Y(b,q) and Z(c,r) be the points such that a , b and c are in AP.… NDA 2026 If (10 + _ 10 x) , (10 + _ 10 y) and (10 + _ 10 z) are in AP, then consider the following… NDA 2025 How many terms of the series 1 + 3 + 5 + 7 + … amount to a sum equal to 12345678987654321… NDA 2025 For the following two (02) items: Let (6 + 10 + 14 + … up to m terms) = (1 + 3 + 5 + 7 +… NDA 2025 For the following two (02) items: Let (6 + 10 + 14 + … up to m terms) = (1 + 3 + 5 + 7 +… NDA 2025 How many terms are identical in the two APs 19, 21, 23, … up to 110 terms and 19, 22, 25… NDA 2025 If p , 1 , q are in AP and p , 2 , q are in GP, then which of the following statements… NDA 2025 The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If r ≠ 1… NDA 2025 If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term… NDA 2025 The sum of the first k terms of a series S is 3k^2 + 5k . Which one of the following is… NDA 2025 What is the harmonic mean of the numbers C(10,3) , C(10,4) , C(10,5) , C(10,6) and… NDA 2025 If 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 PYQs JEE Mathematics PYQs All NDA PYQs