Give 4 #s in an arithmetic sequence, the 1st is 2/3 and the 4th is 1 7/15, what is the 2nd?

Question

i need someone to show me how to figure this out as well as the answer.

Answer 1

10/15, 14/15, 18/15, 22/15

so the 2nd is 14/15

Answer 2

Reminder: an arithmetic sequence is one where the difference between a term and its last is fixed, all the way throughout the sequence. So something like

1, 3, 5, 7, 9

would be an arithmetic sequence, but

1, 2, 4, 8, 16, 32, 64

would not.

In your case, your sequence goes

2/3, ?, ?, 22/15

Convert the 2/3 to having 15 as the denominator.

10/15, ?, ?, 22/15

There's no doubt about it that the two missing numbers are 14/15 and 18/15 (with each term increasing by 4/15)

So the second number in the sequence is 14/15

Answer 3

first convert the fractions to improper with common denominators....

so the first is 10/15 and the fourth is 22/15

the difference between the two is 12/15 so if you do this with three arithmetic steps, each step is 4/15, therefore the second number is 14/15