Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Sequences and Series

NDA 2011 · Mathematics · Sequences and Series

What is the value of 8+2 8+2 8+2 8+ ∞ ?

What is the value of \sqrt{8+2 \sqrt{8+2 \sqrt{8+2 \sqrt{8+\ldots \infty}}}} ?

Options

  1. A1010
  2. B88
  3. C66
  4. D44

Correct answer

D. 44

Step-by-step solution

Let x=8+28+28+28+⋯∞x=8+2x⇒x2=8+2x⇒x2−2x−8=0⇒x2−4x+2x−8=0x=\sqrt{8+2 \sqrt{8+2 \sqrt{8+2 \sqrt{8+\cdots \infty}}}}x=\sqrt{8+2 x}\Rightarrow \quad x^2=8+2 x\Rightarrow \quad x^2-2 x-8=0\Rightarrow \quad x^2-4 x+2 x-8=0x(x−4)+2(x−4)=0(x−4)(x+2)=0\begin{array}{r}x(x-4)+2(x-4)=0 \\ (x-4)(x+2)=0\end{array}x=4,x=−2∴x=4\begin{aligned} x & =4, x=-2 \\ \therefore x & =4\end{aligned}$ \quad[\because x > 0]
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