Answer to Question #71747 in Algebra for Daryl D. Ligutan

Question

1. Alex started training for a 21-km run a month prior to a marathon. In order to build stamina, he decided to gradually increase the distance he runs each training day. On the first day, Alex ran a total of 3 km. On the second and third days, she ran 5 and 7 km respectively. For the succeeding five training days, he ran 9, 11, 13, 15, and 17 km. If he trained for a total of 15 days, determine the total distance he ran.

Answer 1

The first day: a1 = 3 km
The second day: a2 = 5 km
The third day: a3 = 7 km
The 4th day: a4 = 9 km
This sequence is the arithmetic progression where the step (d) is 2. Alex has run for 15 days.
aN = a1 + d*(N-1) is to find N-th term of progression.
a15 = 3+2*(15-1) = 31 km
I have to find the sum of terms for the arithmetic progression: SN = (a1+aN)*N/2
S15 = (3+31)*15/2 = 255 km