How do you find the sum of the geometric sequence 2,4,8...if there are 20 terms?

Question

SlabydouluS62 · Accepted Answer

Sum of GS=Sn=(a(r)n−1)1r−1 where a is the first term, n the no. of terms and r the common ratio a=2,n=20,r=a2a=a3a2=42=84=2 S20=2⋅(220−1)2−1 S20=2⋅(220−1)=2097150

Lakisha Archer · Accepted Answer

Now let us first understand what a geometric series is.
A geometric series is a series in which the ratio of any two consecutive terms is the same.
Hence a geometric series looks like

a + a r + a r^{2} + a r^{3} + \dots + a r^{n}

. where a is the first term and r is the common ratio.
Now consider the given geometric series 2, 4, 8, …
And the common ratio between two consecutive terms is

\frac{8}{4} = \frac{4}{2} = 2

Hence we have a = 2 and r = 2.
Now we know that sum of n terms of GP is given by

S_{n} = \frac{a (r^{n} - 1)}{r - 1}

Hence substituting a = 2 and r = 2 in the above formula we get,

\Rightarrow S_{n} = \frac{2 (2^{n} - 1)}{2 - 1}

The above equation represents the sum of n terms of the given GP.
Now since we want to find the sum of 20 terms we will substitute n = 20.
Hence we get,

\Rightarrow S_{20} = \frac{2 (2^{20} - 1)}{2 - 1}

\Rightarrow S_{20} = 2 (2^{20} - 1)

How do you find the sum of the geometric sequence

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