Common Terminology

Q. Question 4
Find a, b and c such that the following numbers are in AP.
a, 7, b, 23 and c.

Q.

Find the sum of the AP: $2,4,6,...$ upto $100$ terms.

Q. Question 28
If the sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, then find the sum of first 10 terms.

Q. Question 15
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is

A) 0
B) 5
C) 6
D) 15

Q. In an arithmetic progression, the 4th term is 11 and12th term is 35, then first term of the a.p

Q.

Write down the sequence of natural number ending in 1 or 6 and describe it in two ither ways

Q. Question 33
The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is –30 and the common difference is 8. Find n.

Q. Question 3 (i)
Write the first three terms of the AP’s, when a and d are as given below:
$a=\frac{1}{2},d=-\frac{1}{6}$

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

Q.

In any three consecutive terms of an arithmetic sequence, the middle term is ___

1. Twice the difference between its previous term and next term.

2. 4 times the sum of the first and the last term

3. Twice the sum of its previous term and next term.

4. Thrice the sum of the first and the last term

Q.

Question 4 (viii)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(viii) $-\frac{1}{2},-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}\dots \dots$

Q. Question 21 (ii)
Find the sum:
$(4-\frac{1}{n})+(4-\frac{2}{n})+(4-\frac{3}{n})+\cdots uptonterms$

Q.

Question 4 (vii)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(vii) 0, - 4, - 8, - 12 …

Q. Which term of the AP : $121,117,113,...$, is its first negative term
[Hint : Find $n$ for $a_n<0$]

Q. 24. A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one third of the debt unpaid. Find the value of the first instalment.

Q. The sequence of all even numbers is a/an ___ arithmetic progression and that of the first 100 odd numbers is a/an ___ arithmetic progression.

1. infinite, infinite
2. infinite, finite
3. finite, infinite
4. finite, finite

Q. Find the $20th$ term from the last term of the AP $3,8,13,....253.$

1. $156$
   
2. $180$
3. $158$
4. $188$

Q. If the $nth$ term of the AP $9,7,\mathrm{5..}$ is same as the $nth$ term of the AP $15,12,9,...$, find $n.$

1. $7$
2. $9$
3. $8$
4. $10$

Q.

Difference of 7th and 12th terms in an arithmetic sequence is 20, the common difference is

1. 4

2. 6

3. -4

4. 5

Q. The sum up to $n$ terms of an AP with first term $a$, last term $l$ and common difference $d$ is:

1. $\frac{n}{2}[2a+(n-1\left)d\right]$
2. $n[2a+(n-1\left)d\right]$
3. $\frac{n}{2}(a+l)$
4. $n(2a+(n-1\left)d\right)$

Q. The sum up to n terms of an AP with first term $s$, last term $t$ and common difference $d$ is

1. $\frac{n}{2}(2s+(n-1\left)d\right)$
2. $n(2s+(n-1\left)d\right)$
   
3. $\frac{n}{2}(s+t)$
4. $n(2s+(n-1\left)d\right)$

Q. The sum of $11$ terms of an A.P. whose middle term is $30,$ is

1. $330$
2. $320$
3. $340$
4. $350$

Q.

For any AP, the expression for the $n^{th}$ term is always a ___ expression in $n$.

Q. If the nth term of a progression be a linear expression in n then prove that this progression is an AP.

Q. Find the sum of $20$ terms of the AP $1,4,7,10,.....$.

Q. The $4th$ term from the end of the AP
$-11,-8,-5,....................49$ is

1. $37$
2. $40$
3. $43$
4. $58$

Q. If $k,$ $(2k-1)$ and $(2k+1)$ are the three successive terms of an AP, find the value of $k.$

Q. The first term of an AP is 11. The sum of its first four terms is 56, and its last four terms is 112. Find the number of terms in the A.P. [4 MARKS]

Q. The first term of an AP is $-50$ and the $50th$ term is $48$. Find the common difference

1. $4$
2. $1$
3. $-3$
4. $2$

Q.

For an arithmetic sequence, what is the sum of three consecutive terms?

1. twice the middle term

2. twice the first term

3. thrice the middle term

4. thrice the first term