SOLUTION: I have a question. I have been given to find the 15th term, when I know the 3rd term to be 7 and 20th term to 43. I trying to figure the common difference and the what the 15th ter

Algebra ->  Sequences-and-series -> SOLUTION: I have a question. I have been given to find the 15th term, when I know the 3rd term to be 7 and 20th term to 43. I trying to figure the common difference and the what the 15th ter      Log On


   

Question 308365: I have a question. I have been given to find the 15th term, when I know the 3rd term to be 7 and 20th term to 43. I trying to figure the common difference and the what the 15th term is.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
an=a1%2B%28n-1%29%2Ad
.
.
.
a3=a1%2B%283-1%29%2Ad=a1%2B2d=7
a20=a1%2B%2820-1%29%2Ad=a1%2B19d=43
So now you have two equations with two unknowns.
a1%2B2d=7
a1%2B19d=43
You can re-arrange both of them,
a1=7-2d
a1=43-19d
Since they both equal a1, set them equal to each other and solve for d.
7-2d=43-19d
17d=36
d=36%2F17
Then use either equation to solve for a1.
a1=7-2d
a1=7-2%2836%2F17%29
a1=119%2F17-72%2F17
a1=47%2F17
Then the 15th term would be,
a15=47%2F17%2B%2815-1%29%2A%2836%2F17%29
a15=47%2F17%2B504%2F17
+a15=551%2F17+