List of top Mathematics Questions on Geometric Progression asked in JEE Main

If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309, then the sum of its first nine terms is:

Let $ a, ar, ar^2, \dots $ be an infinite G.P. If $$ \sum_{n=0}^\infty ar^n = 57 \quad \text{and} \quad \sum_{n=0}^\infty a^3 r^{3n} = 9747, $$ then $ a + 18r $ is equal to:

If in a G.P. of64terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P., then the common ratio of the G.P. is equal to:

If the range of $f(\theta) = \frac{\sin^4\theta + 3\cos^2\theta}{\sin^4\theta + \cos^2\theta}, \, \theta \in \mathbb{R}$ is $[\alpha, \beta]$, then the sum of the infinite G.P., whose first term is $64$ and the common ratio is $\frac{\alpha}{\beta}$, is equal to ____.

Let $ a $ and $ b $ be two distinct positive real numbers. Let the 11^th term of a GP, whose first term is $ a $ and third term is $ b $, be equal to the $ p $-th term of another GP, whose first term is $ a $ and fifth term is $ b $. Then $ p $ is equal to

If first term of non-constant GP be $\frac 18$ and every term is AM of next two, then $ \displaystyle\sum_{r=1}^{20} T_r- \displaystyle\sum_{r=1}^{18} T_r$ is

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is \[ \frac{70}{3} \] and the product of the third and fifth terms is 49. Then the sum of the $4^\text{th}, 6^\text{th}$, and $8^\text{th}$ terms is:

Let $α$ and $β$ the roots of equation $px^2 + qx - r = 0$, where $P≠ 0$. If $p,q,r$ be the consecutive term of non constant G.P and $\frac{1}{α} + \frac{1}{β} = \frac{3}{4}$ then the value of $(α - β)^2$ is:

Let a₁, a₂, a₃, …. be a G.P. of increasing positive numbers. Let the sum of its 6^th and 8^th terms be 2 and the product of its 3rd and 5th terms be $\frac{1}{9}$ .Then 6 (a₂ + a₄) (a₄ + a₆) is equal to

Let $ S = 109 + \frac{108}{5} + \frac{107}{5^2} + \frac{106}{5^3} + \cdots $. Then the value of $ (16S - (25)^{3}) $ is equal to:

Suppose a₁, a₂, 2, a₃, a4 be in an arithmeticogeometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all 5 terms of the arithmetico-geometric progression is $\frac{49}{2}$ , then a4 is equal to ________ .

If the sum and product of four positive consecutive terms of a GP, are 126 and 1296, respectively, then the sum of common ratios of all such GPs is

The $4^{\text {th }}$ term of $G P$ is $500$ and its common ratio is $\frac{1}{m}, m \in N$ Let $S_n$ denote the sum of the first $n$ terms of this GP If $S_6>S_5+1$ and $S_7< S_6+\frac{1}{2}$, then the number of possible values of $m$ is

For the two positive numbers $a, b$, if $a, b$ and $\frac{1}{18}$ are in a geometric progression, while $\frac{1}{a}, 10$ and $\frac{1}{b}$ are in an arithmetic progression, then $16 a+12 b$ is equal to

Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be 98/25. Then the sum of the first 21 terms of an AP, whose first term is 10ar, n^th term is a_n and the common difference is 10ar², is equal to

For a natural number $n$, let $α_n = 19n – 12n$. Then, the value of $\frac {31α_9−α_{10}}{57α_8}$ is _____.

Consider two G.Ps. $2, 2^2, 2^3, ….$ and $4, 4^2, 4^3, …$ of $60$ and n terms respectively. If the geometric mean of all the $60 + n$ terms is $(2)^{\frac {225}{8}}$ then $\sum_{k=1}^{n}k(n−k)$ is equal to

If a₁ (> 0), a₂, a₃, a₄, a₅ are in a G.P., a₂ + a₄ = 2a₃ + 1 and 3a₂ + a₃ = 2a₄, then a₂ + a₄ + 2a₅ is equal to _______.

Let for n = 1, 2, …, 50, S_n be the sum of the infinite geometric progression whose first term is n² and whose common ratio is
$\frac{1}{(n+1)^2}$ . Then the value of
$\frac{1}{26} + \sum_{n=1}^{50} \left(S_n+\frac{2}{n+1}-n-1 \right)$
is equal to ________.

Let A₁, A₂, A₃, … be an increasing geometric progression of positive real numbers. If A₁A₃A₅A₇ = $\frac {1}{1296}$ and A₂ + A₄ = $\frac {7}{36}$ then, the value of A₆ + A₈ + A₁₀ is equal to