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?

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

To calculate the total distance he runs in the first seven days of training, you need to sum up the distances for each day. However, your mistake lies in incorrectly calculating the distances for each day.

a) On the second day, the runner runs 10% more than the previous day, which is 1.5 km + 10% of 1.5 km.

To calculate 10% of 1.5 km: 10% × 1.5 = 0.1 × 1.5 = 0.15 km

So the distance the runner runs on the second day is: 1.5 km + 0.15 km = 1.65 km

b) Now let's calculate the total distance for the first seven days step-by-step:

Day 1: 1.5 km
Day 2: 1.5 km + 10% of 1.5 km (0.15 km) = 1.5 km + 0.15 km = 1.65 km
Day 3: 1.65 km + 10% of 1.65 km (0.165 km) = 1.65 km + 0.165 km = 1.815 km
Day 4: 1.815 km + 10% of 1.815 km (0.1815 km) = 1.815 km + 0.1815 km = 1.9965 km
Day 5: 1.9965 km + 10% of 1.9965 km (0.19965 km) = 1.9965 km + 0.19965 km = 2.19615 km
Day 6: 2.19615 km + 10% of 2.19615 km (0.219615 km) = 2.19615 km + 0.219615 km = 2.415765 km
Day 7: 2.415765 km + 10% of 2.415765 km (0.2415765 km) = 2.415765 km + 0.2415765 km = 2.6573415 km

Now, let's add up the distances for all seven days:

1.5 km + 1.65 km + 1.815 km + 1.9965 km + 2.19615 km + 2.415765 km + 2.6573415 km = 14.2847555 km

Rounding to one decimal place, the total distance the runner covers in the first seven days is approximately 14.3 km.

To calculate the total distance he runs in the first seven days of training, you need to consider that each day he runs 10% more than the previous day. Let's break down the steps:

a) On the first day, he runs 1.5 km.
b) On the second day, he would run 10% more than the first day. To find out how much that is, multiply 1.5 km by 0.10 (which is equal to 10%). Add this result to the distance on the first day: 1.5 km + (1.5 km * 0.10) = 1.5 km + 0.15 km = 1.65 km.
c) On the third day, he would run 10% more than the second day. To find out how much that is, multiply 1.65 km (distance on the second day) by 0.10. Add this result to the distance on the second day: 1.65 km + (1.65 km * 0.10) = 1.65 km + 0.165 km = 1.815 km.
d) Continue this pattern for the next four days, calculating the distance using the same formula: distance on the current day + (distance on the current day * 0.10).
- Fourth day: 1.815 km + (1.815 km * 0.10) = 1.9965 km.
- Fifth day: 1.9965 km + (1.9965 km * 0.10) = 2.19615 km.
- Sixth day: 2.19615 km + (2.19615 km * 0.10) = 2.415765 km.
- Seventh day: 2.415765 km + (2.415765 km * 0.10) = 2.6573415 km.

To calculate the total distance he runs in the first seven days, add up all the distances:
1.5 km + 1.65 km + 1.815 km + 1.9965 km + 2.19615 km + 2.415765 km + 2.6573415 km = 13.2857555 km.

Therefore, the total distance he runs in the first seven days of training is approximately 13.29 km, not 14.2 km. The calculation you provided has the correct steps but may have a rounding error.