The sum of n terms of a progression is (2n – 1). Show that it is a GP and find its common ratio.
In this question, we will try to rewrite the given sum of the progression like the formula for the sum a G.P. series.
It is given that Sn = ( 2n – 1)
The formula for the sum of a G.P. series is,
By solving the 2 equations together, we can say that
⇒
By corresponding the numbers with the variables, we can conclude
a = 1
r = 2
The G.P. series will therefore look like ⇒ 1,2,4,8,16,……to n terms
∴ The given progression is a G.P. series with the common ration being 2.
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