Sum of First n Terms of an AP

Q.

The sum of $3$ numbers in AP is$18$. If the product of the first and third number is $5$ times the common difference, find the numbers.

Q.

What is the sum of the first 30 odd numbers?

1. 900

2. 875

3. 870

4. 920

Q.

Find the sum of first $24$ terms of the A.P. whose $n^{th}$ term is given by $a_n=3+2n$

1. 568

2. 624

3. 672

4. 564

Q.

The $21st$ term of the A.P. whose first two terms are $-3$ and $4$ is

1. $17$

2. $137$

3. $143$

4. $-143$

Q. The sum of terms of the AP 34 + 32 + 30 + .... + 10 is .

1. 290
2. 286
3. 280
4. 284

Q.

Find the sum of all two-digit numbers greater than $50$, which when divided by $7$ leaves remainder $4$.

Q. Question 1 (iv)
Find the sum of the following APs
(iv) $\frac{1}{15},\frac{1}{12},\frac{1}{10},\dots \dots ,to11terms$

Q. Question 5
Is 0 a term of the AP 31, 28, 25, …? Justify your answer.

Q.

Question 149

Repeater Machine
Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. e.g. Sending a piece of wire through a $(\times 2^4)$ machine is the same as putting it through a $(\times 2)$ machine four times.
So, if you send a 3 cm piece of wire thorugh a $(\times 2{)}^4$ machine, its length becomes $3\times 2\times 2\times 2\times 2=48cm.$ It can also be written that a base (2) machine is being applied 4 times.

What will be the new length of a 4 cm strip inserted in the machine?

Q. Question 18
A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ……… as shown the n figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take $\pi =\frac{22}{7})$

Q.

Question 1 (iii)
Find the sum of the following APs
(iii) 0.6, 1.7, 2.8 , …….., to 100 terms

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 sum of first $24$ terms of the list of numbers whose $n^{th}$ term is given by $a_n=3+2n$.

1. 624

2. 564

3. 672

4. 568

Q. Question 3 (ii)
Write the first three terms of the AP’s, when a and d are as given below:
a = -5, d = - 3

Q.

Question 2 (i)
Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows.
(i) a = 10, d = 10

Q. A spiral is made up of successive semicircles, with centers alternatively at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... as shown in the figure.What is the total length of such a spiral made up of thirteen consecutive semicircles?

1. 140
2. 143
3. 152
4. 163

Q. Question 21 (i)
Find the sum:
1 + (-2) + (-5) + (-8) + . . . + (-236)

Q. Question 1 (v)
Which of the following form an AP? Justify your answer.
$\frac{1}{2},\frac{1}{3},\frac{1}{4},\cdots$

Q.

The sum of the first 100 natural numbers is greater than the sum of the even numbers between 1 and 100 (including 100) by _____.

1. 2200

2. 2400

3. 2500

4. 2700

Q. Question 3 (ii)
In the following APs, find the missing term in the boxes.

Q.

In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in total. Each competitor starts from the pole, picks up the nearest flag, comes back to affix the flag onto the pole, picks up the next flag and continues the same way until all the flags are on the pole. The total distance covered is

1. 760 m

2. 820 m

3. 860 m

4. 740 m

Q.

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

Q. If a(n) represents the $n^{th}$ term of an AP, then which of the following is always true?

1. a(2) + a(4) = a(1) + a(5)
2. a(5) + a(19) = a(6) + a(18)
3. a(1) + a(20) = a(21)
4. None of the above

Q. In an arithmetic progression the third term is four times the first term, and the sixth term is $17$, then ${20}^{th}$ term of the progression is

1. $57$
2. $59$
3. $61$
4. None of these

Q. Find the sum to n terms of the AP 5, 2, -1, -4, -7, ...

1. $\frac{n}{2}(13-3n)$
2. $\frac{n}{2}(30-3n)$
3. $\frac{n}{2}(13+3n)$
4. $n(8-3n)$

Q. If the sum of the first n terms of an AP is given by $S_n=n^2+3n$, then the first term of the AP is

1. 2
2. 1
3. 3
4. 4

Q.

The number of terms in an AP is 10. The $n^{th}$ term of this AP is 50 and the common difference is 2. Find the first term.

1. 30

2. 32

3. 40

4. 50

Q. Find the sum of first 40 positive integers divisible by 6.
(2 marks)

Q. The $n^{th}$ term of an AP is given by $a_n=2+5n$. The sum of the first 10 terms of the AP is .

1. 290
2. 330
3. 350
4. 295

Q. Which of the following numbers lies between $\frac{-5}{2}$ and $\frac{3}{4}$?

1. $1$
2. $-3$
3. $3$
4. $0$