Question

Which of the following are GP. If they are in GP. write next three terms?
1) 5,55,555,.........


2) x, 1, 1/x,.......,(x≠0)

Answer 1

the next 3 terms GP is 5( 1*n +10(n-1) +100*(n-2) +1000 *( n -3) +10000 * (n -4) + 100000 *(n -5) +1000000* ( n-6)......)
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Answer 2

GP here stands for a geometric progression.

Geometric progression is defined as a series in which multiplication sector remains constant.

Here in series x,1,(1/x).......... multiplication factor is const. and=(1/x)

x*(1/x) = 1
1*(1/x) = (1/x)
(1/x)*(1/x) = (1/x²)
(1/x²)*(1/x) = (1/x³)
(1/x³)*(1/x) = (1/x⁴)