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

Answer : A

Explanation

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

Q 2 - Which term of the arrangement 72+63 + 54+ ....is zero?

Answer : B

Explanation

Given series is an A.P. in which a=72 and d = (63-72)= -9
Let the nth term be 0. Then a+ (n-1) d =0 ⇒ 72+ (n-1)*(-9) = 0 ⇒ 72-9n +9 =0
⇒ 9n =81 ⇒ n = 9
∴ 9th term is the given series is 0.

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

Answer : B

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 - Which term of the G.P. 5,10,20,40 ...is 1280?

Answer : B

Explanation

Let T_n = 1280. Then ar (ⁿ⁻ⁱ) = 1280 ⇒ Here a= 5 and r =2
∴ 5*2(ⁿ⁻ⁱ) =1280 ⇒256 = 2(ⁿ⁻ⁱ) =2⁸ ⇒ n-1 =8 ⇒ n= 9

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 few buys National Savings Certificates each year whose worth surpasses the earlier years buy by Rs 400. Following 8 years, she finds that she has obtained declarations whose aggregate face worth is Rs 48000. What is the face estimation of the Certificates acquired by her in the first years?

Answer : D

Explanation

Let the required value be Rs a.
Also d= 400, n = 8 and Sn = 48000.
Sn   = n/2 [2a + (n -1) d] ⇒ 8/2 *[2a + 7 *400] = 48000
⇒ 2a + 2800 = 12000⇒ 2a=9200⇒ a = 4600

Q 9 - If (1²+2²+3²+??+10²) =385, then the value of (2²+ 4² + 6² +......+ 20²) is

Answer : C

Explanation

(2²+4²+6²+...+20²) = (1*2²+2²*2²+3²*2²+...+10²*2²)
= 2²(1²+2²+3²+??..+10²) = (4*385) = 1540.

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