Find the sum of the first 7 terms of the following sequence. Round to the nearest hundredth if necessary.
14, 56,
224, ...

76454

Step-by-step explanation:

Sequence : 14,56,224, ..14(4^(n-1)

where n=term number.

First term: 14*(4^(1-1)) = 14*(4^0) = 14

Second term: 14*(4^(2-1))=14*4 = 56

Third term: 14*(4^(3-1))=14*16 = 224

...

7th term: 14*(4^(7-1)) = 14*(4^6)

Sum of the first 7 terms

= 14*(4^0+4^1+4^2+4^3+4^4+4^5+4^6)

= 14(4^7-1)/(4-1)

= 14(4^7-1)/3

= 76454