Question

Write the next three terms in each of the given geometric progressions (G.P.s):

i) 2, )-1, 2, 4, 8, ... ii) 2, 1/2, 1/8, 1/32,... iii) -12, -6, 0, 6, ...

choose the correct answer

A) (16, 32, 64),(1/16, 1/64, 1/256),(12, 18, 24)

B) (16, 32, 64),(1/128, 1/256, 1/512),(12, 18, 24)

C) (10, 20, 40),(1/16, 1/64, 1/256),(-18, -24, -30)

D) (-10, -20, -40),(1/16, 1/64, 1/256),(-18, -24, -30)

Answer 1

The next three terms of the given geometric progressions are: i) (-16, 32, -64), ii) (1/128, 1/512, 1/2048), and iii) (12, 18, 24). None of the provided answer choices perfectly match these results.

Step-by-step explanation:

To find the next three terms in each given geometric progression (G.P.), we need to determine the common ratio and apply it successively to the last given term of the sequence. Let's examine and extend each series:

1. 2, -1, 2, 4, 8, ...: This is a G.P. with a common ratio of -2 (since each term is multiplied by -2 to obtain the next term). Multiplying 8 by -2 repeatedly gives the next three terms as -16, 32, -64.
2. 2, 1/2, 1/8, 1/32,...: The common ratio here is 1/4. Applying it to the last term (1/32), we get the next three terms as 1/128, 1/512, 1/2048.
3. -12, -6, 0, 6, ...: This series increases by 6 each time. So, the next three terms are 12, 18, 24.

Therefore, the set of next three terms for each sequence are (-16, 32, -64), (1/128, 1/512, 1/2048), (12, 18, 24). Considering the given choices, none of them matches the actual next three terms of the sequences perfectly.