Sample QuestionsArithmetic Progression questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find the sum of odd numbers between 0 and 50.
Find the sum of first 17 terms of an AP whose 4th, and 9th terms are -15 and -30 respectively.
The first and last terms of an AP are $5$ and $45$. If the sum of the terms is $400,$ find the number of the terms and the common difference.
View full solution →Find the 20th term from the end of the AP $3, 8, 13,$ $\ldots\ldots$ $253.$
View full solution →For what value of $n$, are the $n$th terms of two AP's $63,65,67$, $\ldots\ldots$ and $3,10,17$, $\ldots\ldots$ equal?
View full solution →If the $p$th, $q$th and $r$th terms of an AP be $a, b$ and $c$ respectively, then prove that
$a(q-r)+b(r-p)+c(p-q)=0$.
View full solution →How many terms of the AP $17,15,13$, $\ldots\ldots$ must be added to get the sum 72? Explain the double answer.
View full solution →If the first term of an AP is 2 and the sum of the first five terms is equal to one fourth of the sum of the next five terms, then.
(a) show that $t_{20}=112$
(b) find the sum of first 30 terms.
View full solution →The sum of first 16 terms of an AP is 112 and the sum of its next 14 terms is 518 . Find the AP .
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289 , find the sum of first $n$ terms.
View full solution →The 6th term from the end of the AP $ 17,14,11, \ldots -40$ is :
View full solution →The 100th term of the AP $x, x+1, x+2, \ldots$ is :
View full solution →The $n$th term of the AP $ 2,5,8, \ldots$ is :
- A
$3 n+1$
- B
$2 n-1$
- C
$2 n+3$
- D
$3 n-1$
View full solution →The common difference of the AP whose $p$th term is $8 p+1$, is :
View full solution →The 11th term of the $AP -3,-\frac{1}{2}, 2 \ldots$ is :
View full solution →Assertion (A) : Sum of natural numbers up to 100 is 5000 .
Reason (R) : Sum of first $n$ natural numbers is given by $\frac{n(n+1)}{2}$.
View full solution →Assertion (A) : In the AP, 10, 6, 2, $\ldots\ldots$ -42 , the number of terms is 14.
Reason (R) : For an AP, $a, a+d, a+2 d, \ldots \ldots l$, the $n$th term from the end is given by $l-(n-1) d$.
View full solution →Assertion (A) : The sum of first $n$ terms of an AP is given by $S _n=2 n^2-5 n$. The common difference of the AP is 4 .
Reason (R) : Sum of first $n$ terms of an AP is given by $S _n=\frac{n}{2}(a+l)$.
View full solution →Assertion (A) : The 20th term of the AP 5, 8, 11, $\ldots$ is 285.
Reason (R) : For an AP, the $n$th term is given by $T _n=a-(n+1) d$.
View full solution →