SOLUTION: Find the sum of the series 5 + 20 + 80 + ....+ 20 480

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Question 927581: Find the sum of the series 5 + 20 + 80 + ....+ 20 480

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
5+%2B+20+%2B+80++ ....+ 20480
a%5B1%5D=5...first term
if you multiply it by 4 you got second term 20, then if you multiply it by 4 you got third term 80
if we write 4 as 2%5E2, but to get first term we can write 2%5E%282n-2%29
so, general formula is a%5Bn%5D=5%2A2%5E%282n-2%29
now find which term is 20480
20480=5%2A2%5E%282n-2%29
20480%2F5=2%5E%282n-2%29
4096=2%5E%282n-2%29
2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2=2%5E%282n-2%29
2%5E12=2%5E%282n-2%29...if bases same, then
12=2n-2 ...solve for n
12%2B2=2n
14=2n
7=n
also find:
a%5B4%5D=5%2A2%5E%282%2A4-2%29
a%5B4%5D=5%2A2%5E%286%29=320

a%5B5%5D=5%2A2%5E%282%2A5-2%29=5%2A2%5E%288%29=1280
a%5B6%5D=5%2A2%5E%282%2A6-2%29=5%2A2%5E%2810%29=5120

then the sum is:
sum%285%2A2%5E%282n-2%29%2Cn=1%2C7%29=5%2B20%2B80%2B320%2B1280%2B5120%2B20480+=27305