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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 - The twelfth term of the A.P. 14, 9, 4, - 1, - 6....is:

Answer : D

Explanation

 Here a = 14, d = (9 - 14) = -5.
∴ T₁₂ = a + (12 -1) d = a + 11d = 14 + 11 * (-5) = -41.

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

Answer : D

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 - The main term of a number-crunching movement is 6 and its normal distinction is 5. The eleventh term is:

Answer : D

Explanation

Here a =6 and d = 5
T₁₁    = a + (11-1) d = a +10 d = (6+10*5) =56.

Q 4 - (45+46+47....+113+114+115)?

Answer : D

Explanation

Here a=45, d =1 and L=115.
A+ (n-1) d = 115 ⇒ 45+ (n-1) *1 = 115
(n-1 ) = 70 ⇒ n = 71
Sum = n/2 * (a+L) = 71/2 * (45 +115) = 71/2 *160 = (71 *80) = 5680.

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

Answer : C

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 - In a G.P. the primary term is 5 and the regular proportion is 2. The eighth term is:

Answer : C

Explanation

a =5, r = 2
∴ 8th term = a *r⁷ = (5*2⁷) =    5*128 = 640

Q 7 - Three numbers are in G.P. Their whole is 28 and item is 512. The numbers are:

Answer : C

Explanation

Let the number be a/r, a, ar.
Then, a/r* a*ar = 512 ⇒ a³ =8³ ⇒ a =8
8/r+8+8r =28 ⇒ 8/r +8r =20 ⇒ 2/r+2r =5
⇒ 2r²-5r+2 =0 ⇒ 2r²-4r-r+2 =0
⇒ 2r (r-2)- (r-2)=0   ⇒ (r-2)(2r-1) =0
⇒r = 2 or r = 1/2
Numbers are 4,8, 16.

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:

Answer : C

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 - (14² +15² +......+30²) =?

Answer : D

Explanation

We know that (1²+2²+3²+... +a²) = {n(n+1)(2n+1)}/6
Given Exp. = (1²+2²+...+13²+14²+??+30²)-(1²+2²+...+13²)
= (30*31*61)/6 - (13*14*27)/6 = (9455- 819) = 8636

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