Question 983047
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
...