Geometric Sequences | MCQs

Explanation

2 ×  2 = 4

4 ×  2 = 8

8 ×  2 = 16

16 ×  2 = 32

Explanation

2 ×  2 = 4

4 ×  2 = 8

8 ×  2 = 16

16 ×  2 = 32

Explanation

6*3=18

9*5=45

18*7=126

45*9=405 

Explanation

The given sequence appears to be obtained by dividing the previous term by 3:

2187 ÷ 3 = 729

729 ÷ 3 = 243

243 ÷ 3 = 81

81 ÷ 3 = 27

27 ÷ 3 = 9

9 ÷ 3 = 3

Explanation

10 × 4 = 40

40 × 4 = 160

160 × 4 = 640

640 × 4 = 2560

Explanation

Now, let's examine the differences between consecutive terms:

17 − 6 = 11

39 − 17 = 22

72 − 39 = 33

The pattern of differences: +11, +22, +33 → increasing by 11 each time.

Next difference should be: +44

So,

72 + 44 = 116

Explanation: Differences follow a pattern: +11, +22, +33, +44.

Explanation

The formula #S_oo=a_1/(1-r)#

#a_1=-10# and #r=1/2#

#S_oo=-10/(1-1/2)#

#S_oo=-20#

Sh1-9-2023

Explanation

GP series = 4, 8, 16, 32, ... 512.

FORMULA USED:

Tn = ar(n-1)

SOLUTION:

GP series = 4, 8, 16, 32, ... 512.

Tn = ar(n-1)

⇒ 512 = 4 × 2(n - 1)

⇒ 128 = 2(n - 1)

⇒ 27 = 2(n - 1)

Now comparing powers we obtain;

⇒ n - 1 = 7

⇒ n = 8

Explanation

The series obtained by adding the terms of a geometric sequence is called a geometric series

Explanation

The common ratio of a geometric sequence cannot be zero because if it were, the sequence would become a series of zeros, which is not considered a geometric sequence.