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

1 Answer

sankarankalyanam

Jun 19, 2018

#color(indigo)(S_(20) = (a (r^n-1)) / (r - 1) = 2097150#

Explanation:

#"Sum of n terms of a G S = S_n = (a (r)^n-1 ))/ (r-1)#

where a is the first term, n the no. of terms and r the common ratio

#a = 2, n = 20, r = a_2 / a = a_3 / a_2 = 4/2 = 8/4 = 2#

#S_(20) = (2 * (2^(20) - 1)) / (2 -1)#

#S_(20) = 2 * (2^(20) - 1) = 2097150#

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