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 |
Discuss it
AM = (a1+a2+a3+......+an)/n
=(n(a1+an)/2)/n
=(a1+an)/2 = (2 + 30)/2 = 16
Question 2 |
32 | |
88 | |
128 | |
110 |
Discuss it
= 4*[4+7*4]
=128
Question 3 |
13/2 | |
14/3 | |
4 | |
16/5 |
Discuss it
Question 4 |
40 | |
21 | |
20 | |
18 |
Discuss it
= 20
Question 5 |
120 | |
123.5 | |
126.5 | |
118.5 |
Discuss it
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 |
13/2 | |
25/8 | |
19 | |
22/9 |
Discuss it
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 |
Discuss it
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 |
Discuss it
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 |
Discuss it
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 |
Discuss it
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.