# 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 - In the event that the fourth term of a number juggling movement is 14 and its twelfth term is 70, then its first term is:

A - - 10

B - -7

C - 7

D - 10

### Explanation

```  Let the first term of the A.P. be a and common difference be d. then,
a+ 3d = 14 ...(i)    a+11d = 70 ...(ii)
On subtracting (i) from (ii), we get 8d =56    d = 7
Putting d = 7 in (i), we get a+3*7=14 ⇒ a= (14-21) = -7   ∴ First term = -7```

Q 3 - The main term of a number-crunching movement is 6 and its normal distinction is 5. The eleventh term is:

A - 5

B - 41

C - 46

D - 56

### Explanation

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

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 - The total of every single common number from 75 to 97 is:

A - 1598

B - 1798

C - 1958

D - 1978

### Explanation

```Sum = 75+76+77+...+97.
Here a =75, d = (76-75) =1
Let the number of terms be n. Then,
A+ (n-1) d =97⇒ 75 + (n-1)*1 =97 ⇒ (n-1) = 22 ⇒ n= 23.
∴ Sum = 23/2 (75 + 97) = (23/2 *172) = (23 *86 ) = 1978.```

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 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?

A - Rs 4300

B - Rs 4400

C - Rs 4500

D - Rs 4600

### 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

A - 770

B - 1155

C - 1540

D - (385)2

### 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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