ABPS Assignment-1

 ABPS ASSIGNMENT-1

1)  441, 484,?,576, 625

A) 492

C) 526

B) 507

D) 529

Ans-The pattern followed here is,

Given numbers are the squares of the 21, 22, 23, and so on.

441 = 21²;

484 = 22²;

529 = 23²;

576 = 24²;

625 = 25²;

Hence, "529" is the correct answer.

2) 1, 27, 125, 343, ?

A) 400

C) 654

B) 729

D) 967

Ans- 

1 = 1³ ;

27 = 3³ ;

125 = 5³ ;

729 = 9³ ;

Hence, "729" is the correct answer.

3) 69, 55, 26, 13, ?

A) 4

C) 8

B) 20

D) 7

Ans- 

(6×9)+1=55 ;

(5×5)+1=26 ;

(2×6)+1=13;

(1×3)+1=4;

Hence, "4" is the correct answer.

4) 256, ?, 324, 361

A) 286

C) 265

B) 275

D) 289

Ans- 

16² = 256

17² = 289

18² = 324

19² = 361

Hence, "289" is the correct answer.

5) Find the 6th for the series: 3, 9, 27, 81.....

A) 653

C) 729

B) 700

D) 500

Ans- The correct option is B 729

The given sequence is 3, 9, 27, 81…

Let us divide each term of the sequence by the term preceding it:

The 4th term of the sequence = 81

The 5th term of the sequence = 3×( 4th term of the sequence) = 3×81 = 243.

So, the 6th term of the sequence = 3x(5th term of the sequence) = 3x 243 = 729.

6) Find the sum upto to 6th term of the series: 3, 9, 27, 81,.....

A) 1096

C) 1098

B) 1092

D) 2000.

Ans- 

3¹ + 3² + 3³ + 3⁴ + 3⁵ + 3⁶

a = 3 r = 3 n = 6

=a\{(r ^ n - 1) / (r - 1)\}

=3\{(3 ^ 6 - 1) / (3 - 1)\}

=1092.

7) 8, 64, 216, 512, ?

A) 1000

C) 987

B) 576

D) 888

Ans- The pattern followed by the given number series is

0 × (0²) = 0

2× (2²) = 8

4 × (4²) = 64

6× (6²) = 216

8 × (8²) = 512 

10 × (10²) = 1000

The required result will be 1000.

8) 8, 16, 24, 40, 64, ?

A) 100

C) 96

B) 98

D) 104

Ans- 

8+8=16,

16+ 8 = 24, 

24 +16= 40,

40+24= 64

64+40=104

The required result will be 104.

9) Find the 50th term of the series 1, 4, 7,...

A) 134

C) 190

B) 148

D) 156.

Ans- First term = a = 1

Common difference = d = 4 - 1 = 3

Number of terms = n = 50

50th term = a₅₀

aₙ = a + (n - 1) d

⇒ aₙ = 1 + (50 - 1) 3

⇒ aₙ = 1 + 49 (3)

⇒ aₙ = 1 + 147

⇒ aₙ = 148

∴ The 48th term of the AP is 148

10) Find the sum upto 50th term of the series 1, 4, 7,....

A) 3700

C) 3725

B) 3750

D) 3755

Ans- a = 1

d = 4-1=3

n = 50

using Sn = n (2a + (n-1)d]

S50 = 50 [2+ 2 49×3]

25 (2 + 147]

= 25 × 149

S50 = 3725