Question

On the first day he runs 1.5 km. Every day he runs 10% more than the day befor.

a) Write down the distance he runs on the second day of training. ..... 1,5km +0,15 = 1,65 km

b) Calculate the total distance He runs in the first seven days of training.

When I counted my answer is 13,65 km but it is not correct. The answer must be 14,2 km but I relly tried everything and I don't have any idea how I can count this, please please could you help me please? Thank you so much
Can you be aslo so nice and show me steps too, please?

I did :
1 day 1,5 km
2 day 1,5 km + 0,15 = 1,65
3 day 1,5 km + (2x0,15) = 1,8 .........
than added everything together like 1,5 + 1,65 + 1,8 + 1,95 .........2,24 = 13,65
but it is not correct, where is my mistake?

Answer 1

first day he ran 1.5
2nd day he ran 1.5(1.1)
3rd day he ran 1.5(1.1)(1.1) = 1.5(1.1)^2
..
on the 7th day he ran 1.5(1.1)^6

so we have:
1.5 + 1.5(1.1)+ 1.5(1.1^2 + ... + 1.5(1.1)^6
which is a geometric series whose sum is
1.5( 1.1^7 - 1)/(1.1 - 1)
= 1.5(.9487171)/.1
= 14.2307565

doing it the long way I got the same thing