Question

You bike 1 mile the first day of your​ training, 1.5 miles the second​ day, 2.5 miles the third​ day, and 4.5 miles the fourth day. If you continue this​ pattern, how many miles do you bike the seventh​ day?

Answer 1

32.5 miles on the 7th day

Explanation:

1, 1.5, 2.5, 4.5

We need to determine the pattern

We are adding .5 + 1/4(2^n)

Lets check

n=1 .5+ 1/4(2) = .5+ .5 =1

n =2 .5 + 1/4*2^2 = .5 +1 = 1.5

n=3 .5 + 1/4 ( 2^3) = .5 + 8/4 = 2.5

n=4 .5 + 1/4 (2^4) = .5 + 16/4 = 4.5

n = 5 .5 + 1/4 (2^5) = .5 +32/4 = 8.5

n = 6 .5 + 1/4 (2^6) = .5 + 64/4 =16.5

n=7 .5 + 1/4(2^7)= .5 + 1/4(128) = 32.5

They bike 32.5 miles