List of top Mathematics Questions on geometric progression asked in KEAM

The number of terms in the sequence $2, 6, 18, \ldots, 1458$ is:

The first and last term of a G.P. are 7 and 448 respectively. If the sum is 889, then the common ratio is

Let $t_1, t_2, t_3, \ldots, t_{2n}$ be in G.P. with common ratio $r$. Then:

If $\dfrac{4^{n+1} + 16^{n+1}}{4^n + 16^n}$ is the Geometric Mean between $4$ and $16$, then the value of $n$ is:

The sum of the geometric series \(\sqrt{3}+\sqrt{12}+\sqrt{48}+\dots\) up to \(10\) terms is

If \( 1, a, b, c, 16 \) are in geometric progression, then \( \sqrt[3]{abc} \) is equal to

If the numbers \( x, 6, y, 54, 162 \) are in geometric progression, then \( \dfrac{y}{x} \) is equal to

Let $G_1, G_2, G_3$ be geometric means between $l$ and $n$, where $l$ and $n$ are positive real numbers. Then the common ratio is

The sum of first $n$ terms of a G.P. is 1023. If the first term is 1 and the common ratio is 2, then the value of $n$ is

The first three terms in a G.P. are $a, b$ and $c$ where $a \neq b$. Then the fifth term is:

The 25th term of $9, 3, 1, \frac{1}{3}, \frac{1}{9}, \ldots$ is:

The product of first 5 terms of a G.P., whose terms are increasing, is 32. The third term of the G.P. is

Let \( a_1, a_2, a_3, \ldots \) be in G.P. If \( a_1 \cdot a_2 \cdot a_3 = 64 \) and \( a_1 \cdot a_2 \cdot a_3 \cdot a_4 \cdot a_5 = 32 \), then common ratio is

In a G.P., the first and third terms are 4 and 8 respectively. Then the \(21^{\text{st}}\) term is

Let \(a_{n} = 2^{n - 1}, n = 1, 2, 3, \ldots\) . Then the value of the sum \(\sum_{n = 1}^{20} a_{n}\) is equal to

\(a_{1}, a_{2}, \ldots , a_{10}\) are in G.P., and if \(a_{1} + a_{2} = 6, a_{9} + a_{10} = \frac{3}{128}\) then the common ratio of the G.P. is equal to

Three numbers a, b, and c are in G.P. If abc = 27 and a + c = 10, then a² + b² + c² =

In a G.P., $1, \frac{1}{2}, \frac{1}{4}, \ldots$, when the first $n$ number of terms are added, the sum is $\frac{1023}{512}$. Then the value of $n$ is

The sixth term in the sequence \( 3, 1, \frac{1}{3}, \dots \) is:

If the $6^{\text{th}}$ term of a G.P. is $2$, then the product of the first $11$ terms of the G.P. is equal to:

If the product of five consecutive terms of a G.P. is $\frac{243}{32}$, then the middle term is:

Let \( S_1 \) be a square of side 5 cm. Another square \( S_2 \) is drawn by joining midpoints of the sides of \( S_1 \). Square \( S_3 \) is drawn similarly and so on. Then \( \text{Area}(S_1) + \cdots + \text{Area}(S_{10}) \) is

The 5th and 8th terms of a G.P. are 1458 and 54 respectively. The common ratio of the G.P. is

If 4th term of a G.P. is 32 whose common ratio is half of the first term, then the 15th term is