How do you find the sum of #6(2)^(i-1)# from i=1 to 10?

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Answer 1 · 2017-07-30T10:02:52

#S_i = a(r^i - 1)/(r - 1)#

Where r is the common ratio and a is the first term

so, with r = 2 and a = 6 we have:

#S_i = 6(2^i - 1)#

Hence, with i = 10 we have:

#S_10 = 6(2^10 - 1)#

i.e. 6 x 1023 => 6138

The first 10 terms are: 6, 12, 24, 48, 96, 192, 384, 768, 1536 and 3072

And #6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072 = 6138#

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