# Progressions

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Question 1 |

Find the Arithmetic Mean of series: 2, 6, 10, 14, 18, 22, 26, 30.

16 | |

8 | |

64 | |

36 |

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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

=(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

32 | |

88 | |

128 | |

110 |

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Question 2 Explanation:

Sum of AP = (n/2)[2a+(n-1)d]

= 4*[4+7*4]

=128

= 4*[4+7*4]

=128

Question 3 |

Find the AM of series: 10, 7, 4, 1, -2

13/2 | |

14/3 | |

4 | |

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

40 | |

21 | |

20 | |

18 |

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Question 4 Explanation:

Sum of series = (n/2)[2a+(n-1)d]

= 20

= 20

Question 5 |

Find sum of series: 2, 2.5, 3, 3. 5, 4, 4. 5..........11

120 | |

123.5 | |

126.5 | |

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

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

13/2 | |

25/8 | |

19 | |

22/9 |

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Question 6 Explanation:

AM of Series: (2+11)/2

=13/2

=13/2

Question 7 |

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

^{9}[(1-3 ^{10})]/(1-3) | |

18 | |

10 | |

20 |

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Question 7 Explanation:

Sol: Sn=[a(1-r

^{n})]/(1-r) =[1(1-3^{10})]/(1-3) =[(1-3^{10})]/(1-3)Question 8 |

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

1/2 | |

1/3 | |

1/4 | |

1/6 |

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Question 8 Explanation:

Sn=a/(1-r)

= (1/3)/(1-1/3)

=1/2

= (1/3)/(1-1/3)

=1/2

Question 9 |

If the product of n positive integers is n

^{n}, then their sum is:A negative integer | |

Equal to n | |

Equal to n+(1/n) | |

Never less than n ^{2} |

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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 = 3

^{3}. This can also be written as n^{n}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 height of 180 m. After striking the ground, it rebounds (3/5)

^{th}of the height from which it has fallen. The total distance that the ball travels before it comes to rest is:540 m | |

600 m | |

720 m | |

900 m |

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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.

There are 15 questions to complete.