# Progressions

• Last Updated : 16 Sep, 2021

12
 Question 1

Calculate the arithmetic mean of the given series: 2, 6, 10, 14, 18, 22, 26, 30.

 A 8 B 16 C 32 D None of the above
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Question 1 Explanation:

AM = (a1+a2+a3+......+an)/n
=(n(a1+an)/2)/n
=(a1+an)/2 = (2 + 30)/2 = 16

 Question 2
Find the Sum of series: 2, 6, 10, 14, 18, 22, 26, 30
 A 32 B 88 C 128 D 110
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Question 2 Explanation:
Sum of AP = (n/2)[2a+(n-1)d]
= 4*[4+7*4]
=128
 Question 3
Find the AM of series: 10, 7, 4, 1, -2
 A 13/2 B 14/3 C 4 D 16/5
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Question 3 Explanation:
AM = (a1+a2+a3+......+an)/n =(n(a1+an)/2)/n =a1+a2/2 =10-2/2 = 4
 Question 4
Find the Sum of series: 10, 7, 4, 1, -2
 A 40 B 21 C 20 D 18
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Question 4 Explanation:
Sum of series = (n/2)[2a+(n-1)d]
= 20
 Question 5
Find sum of series: 2, 2.5, 3, 3. 5, 4, 4. 5..........11
 A 120 B 123.5 C 126.5 D 118.5
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Question 5 Explanation:
sum of AP = (n/2)[2a+(n-1)d]
n=19, a=2, d=1/2
S = (19/2)[2*2+(19-1)1/2]
=(19/2)[4+9]
=9.5*13 = 123.5
 Question 6
Find Arithmetic Mean of series: 2, 2.5, 3, 3. 5, 4, 4. 5..........11
 A 13/2 B 25/8 C 19 D 22/9
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Question 6 Explanation:

Arithmetic mean AM of the series is given by = (a1+a2+a3+.....+an)/n ……… (1) But the given series is also an AP which sum is given by = (n/2)*(a1+an) ………..(2) From equation (1),(2) we get, AM=(a1+an)/2 AM=(2+11)/2=13/2

 Question 7

Find the sum of series: 1, 3, 9, 27, 81, ..............39

 A [(1-3^(10))]/(1-3) B 18 C 10 D 20
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Question 7 Explanation:

Sol: Sn=[a(1-rn)]/(1-r) =[1(1-310)]/(1-3) =[(1-310)]/(1-3)

 Question 8

Calculate the sum of given series: 1/3, 1/9, 1/27, 1/81.................

 A 1/4 B 1/3 C 1/2 D 1
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Question 8 Explanation:

The given series is an infinite GP, whose sum is given by Sn=a/(r-1) Where, a=first term of series, r=common ratio. Therefore, Sn=(1/3)/(1-1/3) Sn=1/2

 Question 9

For n positive integers, if their product is nn, then what will be their sum?

 A Equal to n+(1/n) B Equal to n C A negative integer D Never less than n2
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Question 9 Explanation:

Clearly, since the given integers are positive, their sum can't be negative.
Also, since the numbers are all integers their sum can't be a fraction.
Let's take 1, 3 and 9. The product of these three integers is 27 = 33
This can also be written as nn where n=3.
As we can see, the sum of these 3 integers is not equal to 3.
Therefore, we are left with the fourth option.

 Question 10

A tennis ball is initially dropped from a building of height 180 m. After striking the ground, it rebounds (3/5)th of the height from which it has fallen.

Calculate the total distance that the ball traveled before it comes to rest.

 A 540 m B 600 m C 900 m D None of the above
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Question 10 Explanation:

The total distance traveled by the ball is the sum of two infinite series: a. Series 1: the distance traveled by the ball when it's falling down b. Series 2: the distance traveled by the ball when it's bouncing up S1 = a1 / (1 - r1) and S2 = a2 / (1 - r2) S1 = 180 / (1 - 3/5) and S2 = (180 * 3/5) / (1 - 3/5) S1 = 180 / (2/5) and S2 = 108 / (2/5) S1 = 180 * 5/2 and S2 = 108 * 5/2 S1 = 450 and S2 = 270 Therefore, S = S1+S2 = 720 m.

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