Progressions

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

Answer: (B)

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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

Answer: (C)

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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

Answer: (C)

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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

Answer: (C)

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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

Answer: (B)

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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

Answer: (A)

Progressions
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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

Answer: (A)

Progressions
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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

Answer: (C)

Progressions
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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

Answer: (D)

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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

Answer: (D)

Progressions
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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.