# Arithmetic Progressions - Class 10 - Mathematics

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## Extra Questions - Arithmetic Progressions | NCERT | Mathematics | Class 10

Frequency of an entry gives ___.

Option A) twice the number of times that particular entry occurs

Option B) reciprocal of number of times that particular entry occurs

Option C) number of times that particular entry occurs

Option D) none of these

**Answer: Option C**

**Frequency of an entry** refers to the **number of times that particular entry occurs** in a dataset. It tells how often a specific value appears. Therefore, Option C correctly completes the statement.

Find the sum to $\mathrm{n}$ terms of the AP:

$ 5, 2, -1, -4, -7, \ldots $

A. $\frac{n}{2}(13-3n)$

B. $n(2-3n)$

C. $\frac{n}{2}(7+3n)$

D. $n(n-2)$

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State True or False: $5,5,5,5,5, \ldots \ldots $ is an arithmetic progression.

A) True

B) False

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Suppose $a$, $b$, $c$ are in A.P. and $a^{2}$, $b^{2}$, $c^{2}$ are in G.P. If $a<b<c$ and $a+b+c=\frac{3}{2}$, then the value of $a$ is

(A) $\frac{1}{2}+\frac{1}{\sqrt{2}}$ (B) $\frac{1}{2}-\frac{1}{\sqrt{2}}$ (C) $\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}$ (D) $\sqrt{2}+\frac{1}{2}$

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If the coefficients of $5^{\text{th}}, 6^{\text{th}}$ and $7^{\text{th}}$ terms in the expansion of $(1+x)^{\mathrm{n}}$ are in A.P., then the value of $n$ is

A. 7 only

B. 14 only

C. 7 or 14

D. None of these

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Find the sum of the first 8 multiples of 3.

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If $a$, $b$, $c$ are in A.P. and $a^{2}$, $b^{2}$, $c^{2}$ are in G.P., such that $a<b<c$ and $a+b+c=\frac{3}{4}$, then the value of $a$ is:

A) $\frac{1}{4}$ B) $\frac{1}{4}-\frac{1}{2 \sqrt{2}}$ C) $\frac{1}{4}+\frac{1}{2 \sqrt{2}}$ D) $\frac{1}{4}-\frac{1}{4 \sqrt{2}}$

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For the AP $-3, -7, -11, \ldots$ can we find directly $a_{30} - a_{20}$ without actually finding $a_{30}$ and $a_{20}$? Give the reason for your answer.