SOLUTION: The sixth term of an AP is 37 and the tenth term 53.Find the first term.

Algebra ->  Sequences-and-series -> SOLUTION: The sixth term of an AP is 37 and the tenth term 53.Find the first term.      Log On


   

Question 855486: The sixth term of an AP is 37 and the tenth term 53.Find the first term.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
MENTAL MATH (for multiple choice tests):
from one number to the next you are adding a common difference.
From the sixth term to the tenth term that common difference was added 4 times because
10-6=4 .
That means that the common difference is
%2853-37%29%2F4=16%2F4=4 .
From the first term to the sixth term that common difference was added 5 times because
6-1=5 .
That means that the common difference (4) was added 5 times, so the first term is
37-5%2A4=37-20=highlight%2817%29 .
That is a lot of words, but you can think through the concepts and calculations much faster than you can explain and write them.

USING FORMULAS (to please the teacher by "showing your work"):
a%5B1%5D= first term
d= common difference
a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad= general formula for term number n.
For n=6 we know that
a%5B6%5D=a%5B1%5D%2B%286-1%29%2Ad=a%5B1%5D%2B5%2Ad=37
For n=10 we know that
a%5B10%5D=a%5B1%5D%2B%2810-1%29%2Ad=a%5B1%5D%2B9%2Ad=53
system%28a%5B1%5D%2B5%2Ad=37%2Ca%5B1%5D%2B9%2Ad=53%29 is solved to get system%28highlight%28a%5B1%5D=17%29%2Cd=4%29