Mercedes rides her bike 10 miles in the first week. She increases the distance she rides by 2 miles each week.

How many miles will she ride over the course of 8 weeks?

Hello.

Mercedes rides her bike 10 miles in the first week. She increases the distance she rides by 2 miles each week.

Sum them all up as an Arithmetic Series:

Sum = N/2 [2F + (N - 1) * D]

Sum = 8/2 [2*10 + (8 - 1) * 2]

Sum = 4 [20 + (7*2) ]

Sum = 4 [20 + 14]

Sum = 4 x 34

Sum = 136 miles - that Mercedes will ride over 8 weeks.

Have a nice day

a (1) = 10 mi

d=2 mi

n=8

a (n) = a (1) + d (n-1)

a (8) = 10 + 2 (8-1) = 10+2*7 = 10+14=24 mi

a (8) = 24 mi

S (n) = (n/2) * (a (1) + a (n))

S (8) = (8/2) * (10 + 24)

S (8) = 4*34 = 136

S (8) = 136 mi

Answer: 136 mi.