Practice Progressions Multiple Choice Questions Quiz-2

Q.1

The common difference of an A.P., the sum of whose n terms is S_n, is

S_n - 2S_{n - 1} + S_{n - 2}
S_n - 2S_{n - 1} - S_{n - 2}
S_n - S_{n - 2}
S_n - S_{n - 1}

Q.2

If k, 2k – 1 and 2k + 1 are three consecutive terms of an AP, the value of k is

-2
3
-3
6

Q.3

The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

Q.4

Two A.P.’s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30^th terms is

Q.5

If the n^th term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is

n(n - 2)
n(n + 2)
n(n + 1)
n(n - 1)

Q.6

The common difference of the A.P. $$\frac{1}{{2b}},$$ $$\frac{{1 - 6b}}{{2b}},$$ $$\frac{{1 - 12b}}{{2b}},$$ . . . . . is

2b
-2b
3
-3

Q.7

Let S denotes the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = S_n – k S_n-1 + S_n-2 then k =

1
2
3
None of these

Q.8

If in an A.P., S_n = n²p and S_m = m²p, where S denotes the sum of r terms of the A.P., then S_p is equal to

$$\frac{1}{2}{p^3}$$
mnp
p³
(m + n)p²

Q.9

Given A = 2⁶⁵ and B = (2⁶⁴ + 2⁶³ + 2⁶² + ..... +2⁰), which of the following is true?

B is 2⁶⁴ larger than A
A and B are equal
B is larger than A by 1
A is larger than B by 1

Q.10

The number of terms of the A.P. 3, 7, 11, 15, ....... to be taken so that the sum is 406 is

Q.11

If S_n denote the sum of the first n terms of an A.P. If S_2n = 3S_n , then S_3n : S_n is equal to

Q.12

Sum of n terms of the series $$\sqrt 2 $$ $$ + $$ $$\sqrt 8 $$ $$ + $$ $$\sqrt {18} $$ $$ + $$ $$\sqrt {32} $$ $$ + $$ ....... is

$$\frac{{n\left( {n + 1} \right)}}{2}$$
$$2n\left( {n + 1} \right)$$
$$\frac{{n\left( {n + 1} \right)}}{{\sqrt 2 }}$$
$$1$$

Q.13

A piece of equipment cost a certain factory 6,00,000. If it depreciates in value, 15% the first year, 13.5% the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?

Rs. 2,00,000
Rs. 1,05,000
Rs. 4,05,000
Rs. 6,50,000

Q.14

What is the sum of the following series? -64, -66, -68, ......, -100

-1458
-1558
-1568
-1664

Q.15

The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.

Q.16

What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?

897
1,64,850
1,64,749
1,49,700

Q.17

The 3^rd and 6^th term of an arithmetic progression are 13 and -5 respectively. What is the 11^th term?

Q.18

How many 2-digit positive integers are divisible by 4 or 9?

Q.19

If the sum of n terms of an A.P. be 3n² + n and its common difference is 6, then its first term is

Q.20

If the sums of n terms of two arithmetic progressions are in the ration $$\frac{{3n + 5}}{{5n + 7}},$$ then their n^th terms are in the ration

$$\frac{{3n - 1}}{{5n - 1}}$$
$$\frac{{3n + 1}}{{5n + 1}}$$
$$\frac{{5n + 1}}{{3n + 1}}$$
$$\frac{{5n - 1}}{{3n - 1}}$$

The common difference of an A.P., the sum of whose n terms is Sn, is

If k, 2k – 1 and 2k + 1 are three consecutive terms of an AP, the value of k is

The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

Two A.P.’s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th terms is

If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is

The common difference of the A.P. $$\frac{1}{{2b}},$$ $$\frac{{1 - 6b}}{{2b}},$$ $$\frac{{1 - 12b}}{{2b}},$$ . . . . . is

Let S denotes the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn – k Sn-1 + Sn-2 then k =

If in an A.P., Sn = n2p and Sm = m2p, where S denotes the sum of r terms of the A.P., then Sp is equal to

Given A = 265 and B = (264 + 263 + 262 + ..... +20), which of the following is true?

The number of terms of the A.P. 3, 7, 11, 15, ....... to be taken so that the sum is 406 is

If Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn , then S3n : Sn is equal to

Sum of n terms of the series $$\sqrt 2 $$ $$ + $$ $$\sqrt 8 $$ $$ + $$ $$\sqrt {18} $$ $$ + $$ $$\sqrt {32} $$ $$ + $$ ....... is

A piece of equipment cost a certain factory 6,00,000. If it depreciates in value, 15% the first year, 13.5% the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?

What is the sum of the following series? -64, -66, -68, ......, -100

The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.

What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?

The 3rd and 6th term of an arithmetic progression are 13 and -5 respectively. What is the 11th term?

How many 2-digit positive integers are divisible by 4 or 9?

If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is

If the sums of n terms of two arithmetic progressions are in the ration $$\frac{{3n + 5}}{{5n + 7}},$$ then their nth terms are in the ration

0 h : 0 m : 1 s

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The common difference of an A.P., the sum of whose n terms is S_n, is

Two A.P.’s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30^th terms is

If the n^th term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is

Let S denotes the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = S_n – k S_n-1 + S_n-2 then k =

If in an A.P., S_n = n²p and S_m = m²p, where S denotes the sum of r terms of the A.P., then S_p is equal to

Given A = 2⁶⁵ and B = (2⁶⁴ + 2⁶³ + 2⁶² + ..... +2⁰), which of the following is true?

If S_n denote the sum of the first n terms of an A.P. If S_2n = 3S_n , then S_3n : S_n is equal to

The 3^rd and 6^th term of an arithmetic progression are 13 and -5 respectively. What is the 11^th term?

If the sum of n terms of an A.P. be 3n² + n and its common difference is 6, then its first term is

If the sums of n terms of two arithmetic progressions are in the ration $$\frac{{3n + 5}}{{5n + 7}},$$ then their n^th terms are in the ration