Sample QuestionsArithmetic Progressions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The first three terms of an $AP$ respectively are $3 y-1,3 y+5$ and $5 y+1$. Then $y$ equals:
Answer: C.
View full solution →If k, $2 k-1$ and $2 k+1$ are three consecutive terms of an $A.P.,$ the value of $k$ is.
Answer: B.
View full solution →The common difference of the $A.P. \frac{1}{p}, \frac{(1-p)}{p}, \frac{(1-2 p)}{p} \ldots \ldots \ldots$ is:
Answer: C.
View full solution →If the $n^{\text {th }}$ term of an $A.P.$ is $(2 n+1)$, then the sum of its first three terms is
Answer: B.
View full solution →In an $AP,$ if $d=-2, n=5$ and $a_n=0$ then the value of $a$ is
Answer: D.
View full solution →What is the common difference of an $A.P.$ in which $a_{21}-a_7=84$ ?
View full solution →Find the $9^{t h}$ term from the end $($towards the first term$)$ of the $A.P.\ 5, 9, 13,..........185.$
View full solution →For what value of $k$ will $k+9,2 k-1,2 k+7$ are the consecutive terms of an $A.P.$?
View full solution →In an $AP,$ if the common difference $(d)=-4,$ and the seventh term $\left(a_7\right)$ is $4 ,$ then find the first term.
View full solution →Find the $11^{\text {th }}$ term of the A.P. $-27,-22,-17$, -12........
View full solution →How many terms of $ A.P. 27,24,21, \ldots$. should be taken so that their sum is zero $( 0 )$?
View full solution →Which term of the progression $20,19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots \ldots$ is the first negative term?
View full solution →How many terms of the $A.P. 18, 16, 14 \ldots$ be taken so that their sum is zero?
View full solution →The $4^{\text {th }}$ term of an $A.P$. is zero. Prove that the $25^{\text {th }}$ term of an $A.P$. is three times its $11^{\text {th }}$ term.
View full solution →In an $AP,$ if $S_5+S_7=167$ and $S_{10}=235, $ then find the $AP,$ where $S_n$ denotes the sum of first terms.
View full solution →The sum of $n$ term of an $A.P$ is $3 n^2+5 n$. Find the $A.P$ and its $15^{\text {th }}$ term.
View full solution →Find the sum of terms of the series $\left(4-\frac{1}{n}\right)+\left(4-\frac{2}{n}\right)+\left(4-\frac{3}{n}\right)+\ldots \ldots$
View full solution →If $m^{t h}$ term of an $A.P.$ is $\frac{1}{n}$ and $n^{t h}$ term is $\frac{1}{m}$, then find the sum of its first $m n$ terms.
View full solution →Which term of $A.P. 3,15,27,39, \ldots \ldots$ will be $132$ more than its $54^{\text {th }}$ term.
View full solution →If the sum of first $7$ terms of an $A.P$. is $49$ and that of its first $17$ terms is $289 ,$ find the sum of first $n$ terms of the $A.P$.
View full solution →If the sum of first $6$ terms of an $A.P$. is $36$ and that of the first $16$ terms is $256,$ find the sum of first $10$ terms.
View full solution →The ratio of the $11^{\text {th }}$ term to the $18^{\text {th }}$ term of an $A.P$. is $2: 3$. Find the ratio of the $5^{\text {th }}$ term to the $21^{\text {st }}$ term. Also, find the ratio of the sum of first $5$ terms to the sum of first $21$ terms.
View full solution →The first term of an A.P is 5 , the last term is 45 and the sum is 400.
Find the number of terms and the common difference.
Find the sum of first 51 terms of an A.P. whose second and third terms are 14 and 18 , respectively
The ratio of the sums of first $m$ and first $n$ terms of an A. P. is $m^2: n^2$.
Show that the ratio of its $m^{th}$ and $n^{th}$ terms is $(2 m-1):(2 n-1)$.
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