# 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 - 105 th term of the A.P. 4, 9/2, 5, 11/2, 6 ....is

A - 56

B - 111/2

C - 119/2

D - 55

### Explanation

``` Here a = 4, d = (9/2-4) = 1/2
T₁0₅ = a+(105-1)*d=4+104*1/2=4+52=56.```

Q 2 - What number of numbers arrive somewhere around 10 and 200 which are precisely separable by 7?

A - 21

B - 23

C - 25

D - 27

### Explanation

```Requisite numbers are 14, 21, 28, 35 .., 196.
This is an A.P. in which a = 14 and d = 7
a +(n-1) d = 196 ⇒  14+(n-1)*7 =196
= (n-1)*7 = 182 ⇒ (n-1) = 26 ⇒ n = 27.```

Q 3 - Aggregate number of whole numbers somewhere around 100 and 200 which are distinct by both 9 and 6 is:

A - 5

B - 6

C - 7

D - 8

### Explanation

```LCM of 9 and 6 = 18
So, each one must be multiple of 18.
Requisite no. is 108,126, 144, 162, 180, 198.
Their no. is 6.```

Q 4 - The total 5+6+7+8+.....+19=?

A - 150

B - 170

C - 180

D - 190

### Explanation

```This is an A.P. in which a = 5, d =1 and L=19.
Let the number of its term be n. Then,
Tṇ = 19 ⇒ a + (n-1) d =19
⇒ 5 + (n-1) * 1 = 19 ⇒ (n-1) =14 ⇒ n= 15.
∴ Sṇ = n/2 * (a+L) = 15/2 *(5+19) = 180.```

Q 5 - In the event that a, a-2,3a are in A.P., Then a=?

A - -3

B - -2

C - 3

D - 2

### Explanation

```Since a, (a-2), 3a are in A.P. , we have
(a-2) - a = 3a - (a-2) ⇒ 2a +2 = -2 ⇒ 2a = -4 ⇒ a = -2.```

Q 6 - The third term of a geometrical progression is 4. The result of initial 5 terms is:

A - 43

B - 4⁴

C - 4⁵

D - None of these

### Explanation

```Let the first term be a and common ratio r. Then ar = 4
Product of 5 first term = a* ar*ar2*ar3 *ar⁴ *= a*r⁴ = (ar2)⁵ = 4⁵```

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 man orchestrates to pay off an obligation of Rs 3600 by 40 yearly portions which are in A.P. At the point when 30 of the portions are paid, he bites the dust abandoning 33% of the obligation unpaid. The estimation of the eighth portion is:

A - Rs 35

B - Rs 50

C - Rs 65

D - None of these

### Explanation

```Total debt = Rs 3600 to be paid in 40 installments.
Debt paid = Rs (3600 * 2/3) = Rs 2400, paid in 30 Installments.
Let the installments. Be a, a+d, a+2d...
S₃₀ = 2400 ⇒ 30/2* [2a +(30-1) d] = 2400⇒ 2a+29d = 160.......(i)
S ₄₀ = 3600 ⇒ 40/2 *[2a + (40 -1) d] = 3600 ⇒ 2a + 39d = 180......... (ii)
On solving (i) and (ii) , we get d = 2 and a = 51.
T₈= (a+7d) = (51 + 7 *2) = 65
∴ 8th installments= Rs 65.```

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

A - 900

B - 11025

C - 13400

D - 14400

```We know that (13+23+33+??+n3) = {n (n-1)/2)2