Question

3. Samantha is training to run a marathon. The first week she runs 4 km each day. The next week, she runs 7 km each day. During each successive week (each week following), each day she runs 3 km farther than she ran the days of the previous week. If she runs for five days each week, what total distance will Sara run in a 12-week training session?

Answer 1

1,230km


Week 1 = 5 x 4km = 20
Week 2 = 5 x 7km = 35
Week 3 = 5 x 10km = 50
Week 4 = 5 x 13km = 65
Week 5 = 5 x 16km = 80
Week 6 = 5 x 19km = 95
Week 7 = 5 x 22km = 110
Week 8 = 5 x 25km = 125
Week 9 = 5 x 28km = 140
Week 10 = 5 x 31km = 155
Week 11 = 5 x 34km = 170
Week 12 = 5 x 37km = 185

= 1230km

Answer 2

The total distance will Sara run in a 12-week training session is 1230 .

What is sum of terms in AP?

An arithmetic progression is a sequence of numbers or variables in which the difference between consecutive terms is the same. There can be an infinite number of terms in an AP.

The formula for finding the sum of first n terms of an AP given in the form of "a, a + d, a+2d, a+3d, ....., a+(n-1)d" is:

$S _{n}$= $\frac{n}{2}$ $[2a + (n-1)d]$

According to the question

Samantha is training to run a marathon.

She runs for five days each week

The first week she runs 4 km each day.  = 5 × 4 = 20

The second week, she runs 7 km each day. = 5 × 7 = 35

During each successive week , each day she runs 3 km farther than she ran the days of the previous week.

The third week, she runs 10 km each day. = 5 ×10 = 50

So on

Sara run in a 12-week training session

As this sequence is in AP  

First term (a) = 20

common difference (d) = 35 - 20

                                      = 15

Now,

Sum of 12 terms in AP

$S _{n}$= $\frac{n}{2}$ × [2a + (n-1)d]

Substituting the values, a = 20, d = 15 and n = 12 in the above formula

$S _{12}$ = $\frac{12}{2}$ × $[2(20) + (12-1)15]$

$S _{12}$ = $6 [40 + (11)15}$

$S _{12}$ = $6 [205]$

$S _{12}$ = $1,230$

Hence, the total distance will Sara run in a 12-week training session is 1230 .

To know more about sum of terms in AP here:

https://brainly.com/question/18756309

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