Q. Which term of the AP : $3,15,27,39,..$. will be $132$ more than its ${54}^{th}$ term.

Q. How many three-digit numbers are divisible by $7$?

Q. Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows:
(i) $a=10,d=10$
(ii) $a=-2,d=0$
(iii) $a=4,d=-3$
(iv) $a=-1,d=$ $\frac{1}{2}$
(v) $a=-1.25,d=-0.25$

Q. What were the features of the education system in ancient India?

Q.

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
(i) The taxi fare after each $km$ when the fare is $Rs.15$ for the first $km$ and $Rs.8$ for each additional $km$.
(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.
(iii) The cost of digging a well after every metre of digging, when it costs $Rs.150$ for the first metre and rises by $Rs.50$ for each subsequent metre.
(iv) The amount of money in the account every year, when $Rs.10000$ is deposited at compound interest at $8\%$ per annum.

Q. An $AP$ consists of $50$ terms of which $3^{rd}$ term is $12$ and the last term is $106$. Find the ${29}^{th}$ term.

Q. The ${17}^{th}$ term of an $AP$ exceeds its ${10}^{th}$ term by $7$. Find the common difference.

Q. Choose the correct choice in the following and justify :
(i) ${30}^{th}$ term of the AP: $10,7,4,...$, is
(A) $97$ (B) $77$ (C) $-77$ (D) $87$
(ii) ${11}^{th}$ term of the AP: $-3,-\frac{1}{2},2$, ...., is
(A) $28$ (B) $22$ (C) $38$ (D) $-48\frac{1}{2}$

Q. Which term of the $AP$ : $3,8,13,18,...,$ is $78$.

Q. If the $3^{rd}$ and the $9^{th}$ terms of an $AP$ are $4$ and $-8$ respectively, then which term of this $AP$ is zero

Q. Check whether $-150$ is a term of the AP : $11,8,5,\mathrm{2.....}$

Q. Determine the $AP$ whose third term is $16$ and the $7^{th}$ term exceeds the $5^{th}$ term by $12$

Q. Find the number of terms in each of the following APs :

Q. Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms.
(i) $2,4,8,16,....$
(ii) $2,\frac{5}{2},3,\frac{7}{2},...$
(iii) $-1.2,-3.2,-5.2,-7.2,...$
(iv) $-10,-6,-2,2,...$
(v) $3,3+\sqrt{2},3+2\sqrt{2},3+3\sqrt{2}$
(vi) $0.2,0.22,0.222,0.2222,....$
(vii) $0,-4,-8,-12,...$
(viii) $-\frac{1}{2},-\frac{1}{2},-\frac{1}{2},-\frac{1}{2},...$
(ix) $1,3,9,27$
(x) $a,2a,3a,4a,...$
(xi) $a,a^2,a^3,a^4,...$
(xii) $\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32},...$
(xiii) $\sqrt{3},\sqrt{6},\sqrt{9},\sqrt{12},...$
(xiv) $1^2,3^2,5^2,7^2,..$
(xv) $1^2,5^2,7^2,73,..$

Q. For the following APs, write the first term and the common difference:
(i) $3,1,-1,-3,....$
(ii) $-5,-1,3,7,.....$
(iii) $\frac{1}{3},\frac{5}{3},\frac{9}{3},\frac{13}{3},....$
(iv) $0.6,1.7,2.8,3.9,...$

Q. For what value of $n$, are the $nth$ terms of two $APs:63,65,67,...$ and $3,10,17$, .... equal?

Q. Two APs have the same common difference. The difference between their ${100}^{th}$ terms is $100$, what is the difference between their ${1000}^{th}$ terms.

Q. In the following APs, find the missing terms in the boxes :

Q. Find the ${31}^{st}$ term of an AP whose ${11}^{th}$ term is $38$ and the ${16}^{th}$ term is $73$.

Q.

Sr. no.	$a$	$d$	$n$	$a_n$
(i)	7	3	8	----
(ii)	-18	----	10	0
(iii)	----	-3	18	-5
(iv)	-18.9	2.5	----	3.6
(v)	3.5	0	105	----

Fill in the blanks in the following table, given that $a$ is the first term, $d$ the common difference and $a_n$ is the $n^{th}$ term of the AP: