Progressions (Sequences & Series) Test

Result

Progressions (Sequences & Series) Test - 1

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Question 1
3 / -1

Find the 15th term of an arithmetic progression whose first term is 2 and the common difference is 3

A
45

B
38

C
44

D
40

Solution
Question 2
3 / -1

What is the sum of the first 15 terms of an A.P whose 11th and 7th terms are 5.25 and 3.25 respectively

A
56.25

B
60

C
52.5

D
none of these

Solution
Question 3
3 / -1

If(1²+2²+3²+…..+10²)=385,then the value of (2²+4²+6² + …+20²) is :

A
770

B
1155

C
1540

D
(385*385)

Solution

(1²+2²+3²+.......10²)=385
(2²+4²+6²+.......+20²) = 2²(1²+2²+ 3²+.....+10² )
=4(385)
=1540
Question 4
3 / -1

In an arithmetic series consisting of 51 terms, the sum of the first three terms is 65 and the sum of the middle three terms is 129. What is the first term and the common difference of the series?

A
64, 9/8

B
32, 8/9

C
187/9, 8/9

D
72, 9/8

Solution
Question 5
3 / -1

The sum of the first 100 numbers, 1 to 100 is divisible by

A
1,2,4,8

B
2 and 4

C
2

D
none

Solution
Question 6
3 / -1

How many terms are there in G.P 3,6,12,24,….,384?

A
9

B
10

C
8

D
7

Solution
Question 7
3 / -1

Four angles of a quadrilateral are in G.P. Whose common ratio is an intiger. Two of the angles are acute while the other two are obtuse. The measure of the smallest angle of the quadrilateral is

A
12

B
24

C
36

D
48

Solution
Question 8
3 / -1

How many numbers between 11 and 90 divisible by 7?

A
10

B
11

C
12

D
13

Solution
Question 9
3 / -1

If Sn denotes the sum of the first n terms in an Arithmetic Progression and S1: S4 = 1: 10
Then the ratio of first term to fourth term is:

A
1 : 3

B
2 : 3

C
1 : 4

D
1 : 5

Solution
Question 10
3 / -1

The sum of the three numbers in A.P is 21 and the product of their extremes is 45. Find the numbers.

A
9, 7 and 5

B
Both (1) and (3)

C
5, 7 and 9

D
None of these

Solution

Let the numbers are be a - d, a, a + d
Then a - d + a + a + d = 21
3a = 21
a = 7
and (a - d)(a + d) = 45
a² - d² = 45
d² = 4
d = +2
Hence, the numbers are 5, 7 and 9 when d = 2 and 9, 7 and 5 when d = -2. In both the cases numbers are the same.