SOLUTION: T3=24 T6=60 FIND THE COMMON DIFF AND THE FIRST TERM (a)

Question 1187638: T3=24 T6=60
FIND THE COMMON DIFF AND THE FIRST TERM (a)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
without going through the formula, you can find the common difference in the following manner.

you are given that A3 = 24 and A6 = 60.
6 - 3 = 3
60 - 24 = 36
36/3 = 12

your common difference is 12.

your first term is A1.
A3 - A1 = 2
24 - 2*12 = 24 - 24 = 0
A1 = 0

A6 - A1 = 5
60 - 5*12 = 60 - 60 = 0
A1 = 0

the common difference is 12.
your first term is 0.

if you wish to use the formula to solve for this, do the followng.

the formula is An = A1 + (n-1) * d

this makes:
24 = A1 + 2 * d
60 = A1 + 5 * d

subtract the first equation from the first to get:
36 = 3 * d
solve for d to get d = 12.

go to either one of the formulas and replace d with 12.
24 = A1 + 24
solve for A1 to get A1 = 0

do the same thing with A6 and you get A1 = 0 as well, as you should, since A1 is the same in both formulas.

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