3, __, __, __, __, __, __, __, 23
There are to be 7 terms between 3 and 23.
That means that the whole sequence is to have 9 terms,
when we count the first term 3 and the last term 23.
So n = 9.
an = a1 + (n - 1)d
Substitute:
a1 = first term = 3
n = 9,
an = a9 = last term = 23,
23 = 3 + (9 - 1)d
23 = 3 + 8d
Subtract 3 from both sides:
20 = 8d
Divide both sides by 8
2.5 = d
So the common difference is d = 2.5,
Add 2.5 to the 1st term, getting 3+2.5 = 5.5 for the 2nd term,
Add 2.5 to the 2nd term, getting 5.5+2.5 = 8 for the 3rd term.
etc., etc.,
3, 5.5, 8, 10.5, 13, 15.5, 18, 20.5, 23
Edwin
