SOLUTION: Ann goes swimming regularly. She wants to improve her fitness, so she decides to swim 10 lengths in the first session and increase the number of lengths she swims by 2 every sessio
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Question 983047: Ann goes swimming regularly. She wants to improve her fitness, so she decides to swim 10 lengths in the first session and increase the number of lengths she swims by 2 every session. When she reaches 50 lengths in a session, she will not increase the number any further. After how many sessions does Ann swim 50 lengths for the first time? Found 2 solutions by swincher4391, josmiceli:Answer by swincher4391(1107) (Show Source):
You can put this solution on YOUR website! This is an example of an arithmetic series with first term 10 and common difference 2. We also have that some nth term is 50.
We can relate the nth term with the 1st term by the following formula:
a_n = a_1 + d(n-1)
Here, a_n = 50, a_1 = 10 and d = 2. This is enough to solve.
50 = 10 + 2(n-1)
40 = 2(n-1)
20 = n-1
21 = n
ANSWER -> So on the 21st session, Anne swims 50 lengths. To see it the long way:
I'll label session # on the left and number of lengths on the right.
1 | 10
2 | 12
3 | 14
4 | 16
5 | 18
6 | 20
7 | 22
8 | 24
9 | 26
10 | 28
11 | 30
12 | 32
13 | 34
14 | 36
15 | 38
16 | 40
17 | 42
18 | 44
19 | 46
20 | 48
21 | 50
22 | 50
23 | 50
...
You can put this solution on YOUR website! 1st session: lengths
2nd session:
3rd session:
4th session:
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Let = the number of the session
The lengths Ann swims at session is:
After 21 sessions, Ann swims 50 lengths
for the 1st time
