# Math

a geometric progression has a third term of 20 and a sum to infinity which is three times the first term. find the first term

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term(3) = ar^2 = 20
a = 20/r^2

a/(1-r) = 3a
1/(1-r) = 3
same as in your previous post, r = 2/3

then a = 20/(4/9(
= 20(9/4) = 45

test:
your sequence is 45 , 30 , 20 , 40/3 , 80/9 , ...
is the third term 20 ? , YES
sum of all terms = 20/(1-2/3)
= 20/(1/3)
= 60 , which is 3 times the first term.
All is good!

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