# Progressions

 Question 1

Calculate the arithmetic mean of the given series: 2, 6, 10, 14, 18, 22, 26, 30. 8 16 32 None of the above

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 32 88 128 110

Question 2-Explanation:
Sum of AP = (n/2)[2a+(n-1)d]
= 4*[4+7*4]
=128
 Question 3

Find the Arithmatic mean of series: 10, 7, 4, 1, -2 13/2 14/3 4 16/5

Question 3-Explanation:

Arithmatic Mean = (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

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..........11 120 123.5 126.5 118.5

Question 5-Explanation:

To, find the number of terms in the Ap
Tn = a+(n-1)*d
11 = 2+(n-1)*0.5
So, we get n = 19

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 13/2 25/8 19 22/9

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 [(1-3^(10))]/(1-3) 18 10 20

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................. 1/4 1/3 1/2 1

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? Equal to n+(1/n) Equal to n A negative integer Never less than n2

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. 540 m 600 m 900 m None of the above

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.

• Last Updated : 27 Sep, 2023