New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Sequences and Series question

2005 · Shift 0 · Q102

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Sequences and Series
2005 · Shift 0 · Q102

Sequences and Series question

2005 · Shift 0 · Q102

JEE MainMathematicsSequences and SeriesMCQ+4 / −1

If

x = \sum\limits_{n = 0}^\infty {{a^n},\,\,y = \sum\limits_{n = 0}^\infty {{b^n},\,\,z = \sum\limits_{n = 0}^\infty {{c^n},} } } \,\,

where a, b, c are in A.P and

\,\left| a \right| \lt 1,\,\left| b \right| \lt 1,\,\left| c \right| \lt 1

then x, y, z are in

A
G.P.
B
A.P.
C
Arithmetic-Geometric Progression
D
H.P.

More from Sequences and Series

Let $T_{r}$ be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers m, n, $m e n, T_{m} = \frac{1}{n} an d T_{n} = \frac{1}{m},$ then a - d equals2004 · MCQ
If 1, $lo g_{9} (3^{1 - x} + 2), lo g_{3} (4. 3^{x} - 1)$ are in A.P. then x equals2002 · MCQ
l, m, n are the $p^{t h}$ , $q^{t h}$ and $r^{t h}$ term of a G.P all positive, $t h e n lo g l lo g m lo g n p q r 111 e q u a l s$ 2002 · MCQ
Fifth term of a GP is 2, then the product of its 9 terms is2002 · MCQ
Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is2002 · MCQ
Let $a_{1}, a_{2}, a_{3}, \dots$ be in an A.P. such that $\sum_{k = 1}^{12} a_{2 k - 1} = - \frac{72}{5} a_{1}, a_{1} e q 0$ . If $\sum_{k = 1}^{n} a_{k} = 0$ , then $n$ is :2025 · MCQ
The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$ . Then the number of terms which are integers in the A.P. is :2025 · MCQ
If the sum of the first 10 terms of the series $\frac{4 \cdot 1}{1 + 4 \cdot 1 ^{4}} + \frac{4 \cdot 2}{1 + 4 \cdot 2 ^{4}} + \frac{4 \cdot 3}{1 + 4 \cdot 3 ^{4}} + \dots .$ . is $\frac{m}{n}$ , where $gcd (m, n) = 1$ …2025 · Numerical