JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(a_{n}\) be the \(n^{\text {th }}\) term of a G.P. of positive terms. If \(\sum\limits_{n=1}^{100} a_{2 n+1}=200\) and \(\sum\limits_{n=1}^{100} a_{2 n}=100,\) then \(\sum\limits_{n=1}^{200} a_{n}\) is equal to
- A \(225\)
- B \(175\)
- C \(300\)
- D \(150\)
Answer & Solution
Correct Answer
(D) \(150\)
Step-by-step Solution
Detailed explanation
\(\sum_{n=1}^{100} a_{2 n+1}=200 \Rightarrow a_{3}+a_{5}+a_{7}+\ldots .+a_{201}=200\) \(\Rightarrow \operatorname{ar}^{2} \frac{\left(\mathrm{r}^{200}-1\right)}{\left(\mathrm{r}^{2}-1\right)}=200\) \(\sum_{n=1}^{100} a_{2 n}=100 \Rightarrow a_{2}+a_{4}+a_{6}+\ldots+a_{200}=100\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If the number of terms in the expansion of \({\left( {1 - \frac{2}{x} + \frac{4}{{{x^2}}}} \right)^n},x \ne 0\) is \(28\) then the sum of the coefficients of all the terms in this expansion, is :JEE Mains 2016 Hard
- An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on the is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered \(1, 2, 3,….., 9\) is randomly picked and the number on the card is noted. The probability that the noted number is either \(7\) or \(8\) isJEE Mains 2019 Hard
- Let three vectors \(\vec{a}, \overrightarrow{\mathrm{b}}\) and \(\vec{c}\) be such that \(\vec{a} \times \overrightarrow{\mathrm{b}}=\vec{c}, \overrightarrow{\mathrm{b}} \times \vec{c}=\vec{a}\) and \(|\vec{a}|=2\) Then which one of the following is not true?JEE Mains 2021 Medium
- Let a plane \(P\) pass through the point \((3,7,-7)\) and contain the line, \(\frac{x-2}{-3}=\frac{y-3}{2}=\frac{z+2}{1} .\) If distance of the plane \(P\) from the origin is \(d\), then \(d^{2}\) is equal to \(.....\)JEE Mains 2021 Medium
- An integer is chosen at random from the integers \(\{1,2,3, \ldots \ldots . .50\}\). The probability that the chosen integer is a multiple of atleast one of \(4,6\) and \(7\) isJEE Mains 2024 Medium
- The shortest distance between the \(z-\) axis and the line \(x + y + 2z - 3\, = 0 \,= 2x + 3y + 4z - 4\), isJEE Mains 2015 Hard
More PYQs from JEE Mains
- The number of 4-letter words, with or without meaning, which can be formed using the letters of 'PQRPQRSTUVP', is:JEE Mains 2026 Hard
- The distance of the point \((1,-2,3)\) from the plane \(x-y+z=5\) measured parallel to a line, whose direction ratios are \(2,3,-6\) is :JEE Mains 2021 Hard
- Let \(f(x)=(x+3)^2(x-2)^3, x \in[-4,4]\). If \(M\) and \(m\) are the maximum and minimum values of \(f\), respectively in \([-4,4]\), then the value of \(M-m\) is :JEE Mains 2024 Hard
- If \(A\, = \,\left[ {\begin{array}{*{20}{c}}
1&2&x\\
3&{ - 1}&2
\end{array}} \right]\) and \(B\, = \,\left[ {\begin{array}{*{20}{c}}
y\\
x\\
1
\end{array}} \right]\) be such that \(AB\, = \,\left[ {\begin{array}{*{20}{c}}
6\\
8
\end{array}} \right],\) thenJEE Mains 2014 Hard - Let \(\mathrm{L}_1: \frac{x-1}{1}=\frac{y-2}{-1}=\frac{z-1}{2}\) and \(\mathrm{L}_2: \frac{x+1}{-1}=\frac{y-2}{2}=\frac{z}{1}\) be two lines.
Let \(L_3\) be a line passing through the point \((\alpha, \beta, \gamma)\) and be perpendicular to both \(L_1\) and \(L_2\). If \(L_3\) intersects \(\mathrm{L}_1\), then \(|5 \alpha-11 \beta-8 \gamma|\) equals :JEE Mains 2025 Hard - A committee of \(11\) members is to be formed from \(8\) males and \(5\) females. If \(m\) is the number of ways the committee is formed with at least \(6\) males and \(n\) is the number of ways the committee is formed with at least \(3\) females, thenJEE Mains 2019 Hard