(B) The sum of $n$ terms of an $A.P.$ is given by $S_n = 3n^2 + 5n$.We know that the $m^{th}$ term $T_m$ is given by $T_m = S_m - S_{m-1}$.Given $T_m

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(B) The sum of $n$ terms of an $A.P.$ is given by $S_n = 3n^2 + 5n$.We know that the $m^{th}$ term $T_m$ is given by $T_m = S_m - S_{m-1}$.Given $T_m = 164$,we have:$164 = (3m^2 + 5m) - [3(m-1)^2 + 5(m-1)]$$164 = (3m^2 + 5m) - [3(m^2 - 2m + 1) + 5m - 5]$$164 = 3m^2 + 5m - [3m^2 - 6m + 3 + 5m - 5]$$164 = 3m^2 + 5m - [3m^2 - m - 2]$$164 = 3m^2 + 5m - 3m^2 + m + 2$$164 = 6m + 2$$6m = 162$$m = 27$.

Competitive Quantitative Aptitude Progression and Sequence Progression and Sequence

Easy

If the sum of $n$ terms of an $A.P.$ is $3n^2 + 5n$ and $T_m = 164$,then $m = $

A
$26$
B
$27$
C
$28$
D
None of these

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Progression and Sequence

Find the sum of the first $7$ terms of a $GP,$ whose first term is $1024$ and the common ratio is $\frac{1}{2}$.

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If $4^{th}$ and $8^{th}$ terms of a $G.P.$ are $24$ and $384$ respectively,then find out the first term and common ratio.

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If the first term of an $A.P.$ is $10$,the last term is $50$,and the sum of all the terms is $300$,then the number of terms is:

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If $x, y, z \in \mathbb{R}^+$ such that $x + y + z = 4$,then the maximum possible value of $xyz^2$ is

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If ${A_1}, {A_2}$; ${G_1}, {G_2}$ and ${H_1}, {H_2}$ are $AMs$,$GMs$,and $HMs$ between two quantities,then the value of $\frac{{G_1 G_2}}{{H_1 H_2}}$ is

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If the sum of $n$ terms of an $A.P.$ is $3n^2 + 5n$ and $T_m = 164$,then $m = $

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Find the sum of the first $7$ terms of a $GP,$ whose first term is $1024$ and the common ratio is $\frac{1}{2}$.

If $4^{th}$ and $8^{th}$ terms of a $G.P.$ are $24$ and $384$ respectively,then find out the first term and common ratio.

If the first term of an $A.P.$ is $10$,the last term is $50$,and the sum of all the terms is $300$,then the number of terms is:

If $x, y, z \in \mathbb{R}^+$ such that $x + y + z = 4$,then the maximum possible value of $xyz^2$ is

If ${A_1}, {A_2}$; ${G_1}, {G_2}$ and ${H_1}, {H_2}$ are $AMs$,$GMs$,and $HMs$ between two quantities,then the value of $\frac{{G_1 G_2}}{{H_1 H_2}}$ is

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