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.
Mark the correct alternative in the following:
If the sum of three consecutive terms of an increasing $A.P.$ is $51$ and the product of the first and third of these terms is $273$, then the third term is:
Answer: C.
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If four numbers in $A.P.$ are such that their sum is $50$ and the greatest number is $4$ times, the least, then the numbers are:
- ✓
$5, 10, 15, 20$
- B
$4, 101, 16, 22$
- C
$3, 7, 11, 15$
- D
Answer: A.
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The common difference of the $A.P.$ is $\frac{1}{2\text{q}},\frac{1-2\text{q}}{2\text{q}},\frac{1-4\text{q}}{2\text{q}}, .....$ is
Answer: A.
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The next term of the $A.P. \sqrt{7},\sqrt{28},\sqrt{63},\ .....$
- A
$\sqrt{70}$
- B
$\sqrt{84}$
- C
$\sqrt{97}$
- ✓
$\sqrt{112}$
Answer: D.
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The common difference of the $A.P. \frac{1}{3},\frac{1-3\text{b}}{3},\frac{1-6\text{b}}{3}, ....$ is
- A
$\frac{1}{3}$
- B
$-\frac{1}{3}$
- ✓
$-\text{b}$
- D
$\text{b}$
Answer: C.
View full solution →Which of the following sequences are arithmetic progressions. For those which are arithmetic progressions,
find out the common difference.
$3, 3, 3, 3$, .....
View full solution →Find the sum of the first $25$ terms of an A.P. whose $n^{\text {th }}$ term is given by $a_n=2-3 n$.
View full solution →Find the sum:
$18+15\frac{1}{2}+13\ + ..... \ +\Big(-49\frac{1}{2}\Big)$
View full solution →The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another A.P. whose first term is -30 and common difference is 8. Find n.
Find the $8^{th}$ term from the end of the A.P. $7, 10, 13,... 184.$
View full solution →The general term of a sequence is give by $a_n = -4n + 15.$ Is the sequence an A.P.?
If so, find its $15^{th}$ term and the common difference.
View full solution →Find:$9^{th}$ term of the A.P. $\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4}, .....$
View full solution →Sum of 13 terms of the A.P. -6, 0, 6, 12, .....
Find the sum of the first $15$ terms of each of the following sequences having $n^{th}$ term as:
$b_n = 5 + 2n.$
View full solution →Find the sum of the first $15$ terms of each of the following sequences having $n^{th}$ term as:
$y_n = 9 - 5n.$
View full solution →How many terms are there in the A.P.?
$-1,\frac{5}{6},\frac{2}{3},\frac{1}{2}, .....\frac{10}{3}.$
View full solution →The $24^{\text {th }}$ term of an A.P. is twice its $10^{\text {th }}$ term. Show that its $72^{\text {nd }}$ term is $4$ times its $15^{\text {th }}$ term.
View full solution →All integers from $1$ to $500$ which are multiplies of $2$ or $5$.
View full solution →The $26^{th}, 11^{th}$ and last term of an A.P. are $0, 3$ and $-\frac{1}{5},$ respectively. Find the common difference and the number of terms.
View full solution →Find the sum of the following arithmetic progressions:$\frac{\text{x}-\text{y}}{\text{x}+\text{y}}\frac{3\text{x}-2\text{y}}{\text{x}+\text{y}}\frac{5\text{x}-3\text{y}}{\text{x}+\text{y}}, .....\text{ to n terms.}$
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