Question

Which of the following are GP .if they are in GP write next 3 terms?
i) x,1,1/x,......,(x≠0)
ii)1/✓2,-3,4√2......
iii)0.4,0.04,0.004.......
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Answer 1

Answer:

i) it is in gp. because:

(1 ÷ x) = (1/x) ÷ 1 = 1/x

To get next 3 terms, multiply by 1/x

4th term= (1/x)(1/x) = 1/x²

5th term = (1/x²)(1/x) = 1/x³

6th term = 1/x⁴

ii) It is not in gp

iii) it is in gp. 0.04÷0.4 = 0.004÷0.4 = 0.1

So, to get next terms, multiply by 0.1

4th term = 0.004 x 0.1 = 0.0004

similarly,

5th term = 0.00004

6th term = 0.000004

Answer 2

Your answer :

iii)Here first term is (a) = 0.4

Common ratios are equal so the given series is in GP.

a4 = a r3 = 0.4×(0.1)3 = 0.0004

a5 = a r4 = 0.4×(0.1)4 = 0.00004

a6 = a r5 = 0.4×(0.1)5 = 0.000004