Question

find the sum of the first 20 terms of a geometric series if the first term is 1 and r=2

Answer 1

Given, First term of the given GP = a  = 1

Common ratio of the given GP = r = 2

Number of terms or n = 20

We know,

Sum of n terms = $\dfrac{a(r^{n}-1)}{r-1}$

            Substituting values from question : -

Sum of n terms =$\dfrac{1( 2^{20} -1)}{2 -1 }$

Sum of n terms = $2^{20} -1$

Therefore, sum of 20 terms of GP is $2^{20}-1$

Answer 2

$\huge \bold {\mathfrak {hey}}$

✔️ Given :
➡️ First term of GP =1
➡️ Ratio = r =2

Number of terms = n



Formula

$sum \: of \: n \: terms \: = \frac{a( {r}^{n} - 1) }{r - 1}$


Substitute values


➡️ 1( 2 ^ 20 - 1) / 2 - 1

➡️ 2 ^ 20 - 1


Therefore the sum of 20 terms GP is 2 ^20 - 1


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