# Progression - Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to Progression. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.

Q 1 - What number of term arrives in the A.P. 7, 11, 15..... 139?

A - 33

B - 34

C - 32

D - 31

### Explanation

Here a = 7 and d = (11-7) = 4
Let there be n terms in the given A.P. then,
Tn = 139 ⇒a+ (n-1) d =139
⇒ 7+ (n-1)*4 = 139 ⇒ (n-1) *4 = 132 ⇒ (n-1) = 33
⇒ n = 34

Q 2 - In the event that 2x (x+10) and (3x +2) are in A.P. at that point x=?

A - 4

B - 5

C - 6

D - 8

### Explanation

Since 2x, (x+10) and (3x+2) are in A.P. we have
(x+10)-2x = (3x+2)-(x+10) ⇒ 10-x =2x-8 ⇒ 3x= 18 ⇒ x= 6

Q 3 - What number of products of arrive between the whole numbers 15 and 105, both comprehensive?

A - 30

B - 31

C - 32

D - 33

### Explanation

Requisite no. are 15, 18, 21, 24, 105.
Here a = 15 and d = (18-15) = 3
Let their number be n. Then,
a + (n-1) d =105 ⇒ 15+ (n-1)*3 = 105
⇒ a+ (n-1) d = 105 ⇒ 15+ (n-1)*3 = 105
⇒ (n-1)*3 = 90   ⇒ n-1 =30 ⇒ n = 31

Q 4 - What is the following number in the math movement 2, 5, 8....?

A - 7

B - 9

C - 10

D - 11

### Explanation

This is an A.P. in which a = 2 and d = (5-2) =3.
∴ Next number= (8+3) =11.

Q 5 - What number of odd number pages arrives in a book of 1089 pages?

A - 542

B - 544

C - 545

D - 546

### Explanation

The pages are 1, 3, 5, 7...,1089.
This is an A.P. in which a= 1, d = (3-1) = 2 and L = 1089.
Let the number of these term be n. then,
(a+ (n-1) d = 1089 ⇒ 1 + (n - 1)* 2 = 1089 ⇒ (n-1 ) * 2 = 1088
n-1 =544⇒ n = 545.
∴ Required number of pages=545.

Q 6 - What number of term of the series 3,9,27 ... will mean 363?

A - 5

B - 6

C - 7

D - 8

### Explanation

Given series is a G.P. in which a =3, r= 3 and Sn =363
∴ Sn = a (rⁿ-1)/(r-1) ⇒ 3*(3ⁿ-1)/ (3-1) = 363 ⇒ 3ⁿ-1 = 363*2/3 = 242
3ⁿ= 243 = 3⁵⇒ n =5

Q 7 - In the event that a ≠b, Then which of the accompanying proclamations is valid?

A - a+b/2= √ab

B - a+b/2< √ab

C - a+b/2> √ab

D - All of these

### Explanation

For any two unequal numbers a and b, we have (A.M).> (g.m)
∴   (a+b)/2 > √ab

Q 8 - A whelp comprises of individuals whose ages are in A.P., the normal contrast being 3 months .If the most youthful of the club in not more than years old and the sum of the age of the considerable number of recollects is 250 years, then the no. of recall in the club is :

A - 15

B - 20

C - 25

D - 30

### Explanation

Let the ages be 7 years, 29/4 years, 15/2 years and so on.
The ages are in A.P. in which a=7, d= 1/4 and Sn= 250
Sn = n/2[2a+ (n-1) d] ⇒ n/2 [2*7+ (n-1)*1/4] =250
⇒ n [14+ (n-1)/4] = 250
⇒ n [14+ (n-1)/4 ]=500 ⇒ n[56+(n-1) = 2000
⇒ n (n+55) = 2000 ⇒ n2 +55n-2000 = 0
⇒ n2+80n -25n -2000 = 0 ⇒ n (n+80)-25 (n+80) = 0
⇒ (n+80) (n-25) = 0 ⇒ n= 25(∵ n ≠-80)
∴ Number of members in the club= 25

Q 9 - (13 +23 + 33+...... + 153) =?

A - 900

B - 11025

C - 13400

D - 14400