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

Answer : C

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 - The eighth term of the G.P. 2, 6, 18 ...is:

Answer : C

Explanation

Here a = 2 and r = 6/2 =3.
8th term = [a*r (⁸⁻ⁱ)] = ar ⁷ = 2*3⁷ = 2*(2187) = 4374

Q 6 - In the event that the fourth and ninth term of a G.P. is 54 and 13122 separately, there its second term is:

Answer : A

Explanation

Let its 1st term be a and common ratio r. Then,
ar³ = 54 and ar⁸ = 13122
∴ ar⁸/ ar³ = 13122/54 ⇒ r⁵ =243 = 3⁵ =r = 3
∴ a* 3³ = 54 ⇒ a*27 = 54 = > a =2
2nd term = ar = (2*3) =6

Q 7 - A man needs to pay Rs 975 in yearly portion every portion being not exactly the prior one by Rs 5. The measure of first portions is Rs 100. In what time, the whole sum will be paid?

Answer : C

Explanation

Let the requisite time be n years.
Then, a =100 and d=-5
Let the number of terms be n. Then,
n/2 *[2a+ (n-1)d]  = 975
⇒ n/2 [200+ (n-1)*(-5) = 975   ⇒ n (205-5n) = 1950
⇒ 5n² -205n +1950= 0 ⇒ n²- 41n+ 390 =0
⇒ n² -26n-15n+ 390 = 0 ⇒ n (n-26) -15(n-26) = 0
⇒ (n-15) (n-26) = 0 ⇒ n= 15.   [∵n ≠ 26]

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 - In the event that (1² + 2² + 3²+ ......... + x²) = x(x+1) (2x+1)/6, then (1² + 3²+ 5² + ...... + 19²) =?

Answer : A

Explanation

(1²+ 3²+5²+..........+19²) = (1²+2²+3²+4²+5²+........+18²+19²) - (2²+4²+6²+.........+18²)
 = {19*(19+1) (38+1)/6} - (1*2²+2²*2²+2²*3²+2²*4²+???. +2²*9²)
= 2470 -2²*{1²+2²+3²+... +9²} = 2470 - (4*9*10*19)/6= (2470-1140) =   1330

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