General Form of an AP

Q. Question 1 (ii)
In which of the following situations does the list of numbers involved make an arithmetic progression and why?
(ii) The amount of air present in a cylinder when a vacuum pump removes $\frac{1}{4}$ of the air remaining in the cylinder at a time.

Q.

A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find :
(i) the production in the $1^{st}$ year
(ii) the production in the ${10}^{th}$ year
(iii) the total production in first $7$ years

Q.

In an AP the sum of first n terms is $3n^2÷2+5n÷2$ then find the ${25}^{th}$ term.

Q. If $a_1,a_2,a_3,\dots$ is an arithmetic progression with common difference 1 and $a_1+a_2+a_3+\dots \dots +a_{98}=137$, then what is the value of $a_2+a_4+a_6+\dots \dots +a_{98}$? [2 MARKS]

Q.

If five times the fifth term of an A.P. is equal to 8 times its eighth term, show that its ${13}^{th}$ term is zero.

Q.

If $m$ arithmetic means and three geometric means are inserted between $3$ and $243$ such that $4^{\mathrm{th}}$ A.M. is equal to $2^{\mathrm{nd}}$ G.M., then $m$ is equal to

Q. Question 10
What is the common difference of an AP in which
$a_{18}-a_{14}=32?$

A) 8
B) -8
C) -4
D) 4

Q. An arithmetic progression 5, 12, 19.....has 50 terms.Find its last term.Hence find the sum of its last 15 terms.

Q.

What is the $n^{th}$ term in arithmetic progression?

Q.

Determine the $n^{th}$ term of the AP whose 7th term is −1 and 16th term is 17.

Q.

If $\frac{\text{(a+b)}}{(1-\mathrm{ab})}\text{, b,}\frac{\text{(b+c)}}{(1-\mathrm{bc})}$ are in AP, then $\text{a,}\frac{\text{1}}{b}\text{, c}$ are in

1. $\text{A.P}$

2. $\text{G.P}$

3. $\text{H.P}$

4. None of these

Q.

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

Q. Question 19
Find the sum of the two middle most terms of the AP $-\frac{4}{3},-1,-\frac{2}{3},\cdots ,4\frac{1}{3}$

Q. If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)

Q.

Find the 17th term from the end of the ap 1, 6, 11, 16... 211, 216

Q. The ${13}^{th}$ term of an AP is four times its $3^{rd}$ term.If its fifth term is 16, then find the sum of its first ten terms.

Q.

The sum of the first and third term of an arithmetic progression is $12$ and the product of first and second term is $24$, then first term is

1. $1$

2. $8$

3. $4$

4. $6$

Q.

The sum of three terms of an A.P is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.

Q.

Find the ${12}^{th}$, ${24}^{th}$ and $n^{th}$ term of the A.P. given by 9, 13, 17, 21, 25, .........

Q. Sum of three numbers in AP is 15 and sum of their squars is 93 find the numbers

Q.

If $a,b,c$ are in arithmetic progression, then $\frac{1}{bc},\frac{1}{ac},\frac{1}{ab}$ will be in

1. Arithmetic progression

2. Geometric progression

3. Harmonic progression

4. None of these

Q.

Can (a-3d), (a-d), (a+d), (a+3d) be taken as four consecutive terms in AP?

Q. How many terms are there in the AP: -10, -5, 0, ...50?

1. 12
2. 13
3. 7
4. 8

Q. If 4 times the 4th term of an AP is equal to 18 times its 18th term then find its 22nd term. [CBSE 2012]

Q. Find:

(i) the 20th term of the AP 9, 13, 17, 21, ... .
(ii) the 35th term of the AP 20, 17, 14, 11, ... .
(iii) the 18th term of the AP $\sqrt{2},\sqrt{18},\sqrt{50},\sqrt{98}$, ... .
(iv) the 9th term of the AP $\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4}$, ... .
(v) the 15th term of the AP −40, −15, 10, 35, ... .

Q. In an arithmetic progression of 50 terms , the sum of first ten terms is 210 and the sum of last fifteen terms is 2565 . Find the arithmetic progression .

Q.

The two geometric means between the number $1$ and $64$ are

1. $1$ and $64$

2. $4$ and $16$

3. $2$ and $16$

4. $8$ and $16$

Q. Question 25
In an AP, if $S_n=3n^2+5n$ and $a_k=164$ , then find the value of $k$.

Q.

The sum of $1$st, $3$rd and $17$th term of AP is $216.$ find the sum of the first $13$ terms of the AP.

Q. Find the sum of 2n terms of the series 1^2-2^2+3^2-4^2+5^2-6^2...