SOLUTION: Don't understand sequences, can anyone help? Evaluate this sum: S= 15 + 9 + 27/5 + 81/25 +.......

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Question 169216: Don't understand sequences, can anyone help?
Evaluate this sum:
S= 15 + 9 + 27/5 + 81/25 +.......

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
ahhhhhhh they tried to be tricky on this one....well it simple enough to see we are working with 3's and 5's and that the numerator term say in 27/5 is 3%5E3 while the denominator is 5%5E1 and the next term 81/25 is numerator is 3%5E4 while the denominator is 5%5E2, meaning the terms 3 and 5 are increasing by 1 each time. Its the 1st two terms that are the tricky ones but if you back the exponents up on each of the numerator and denominator making 9= 3%5E1%2F5%5E0 then things begin to make some sense since5%5E0=1. For 15 you would write this as3%5E1%2F5%5E%28-1%29=15
so now its easy to see the pattern which is 3%5En%2F5%5E%28n-2%29 where n is natural numbers starting with 1