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

Question 855491: The sixth term of an AP is 37 an the tenth term 53.Find the sum of the first twenty terms.
Answer by KMST(5328) (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
.
That means that the common difference is
.

In an AP, the 1st and 20th terms
add to the same sum as
the 2nd and 19th terms,
the 3rd and 18th terms, and so on until we get to
the 10th and 11th terms, in the middle of the first 20 terms.
The 10th term is as we were told,
and the 11th term is .
The sum of 20 first terms is made of the 10 sums listed above,
and each of those sums is .
So the sum of the first 20 terms is
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"):
= first term
= common difference
= general formula for term number .
For we know that

For we know that

is solved to get
Then we apply some formula for the sum of the first terms.
Maybe the formula you were given is
(or some variation of that).
Or maybe you were given
(or some variation of that).
With and

you would calculate the 20th term as

and then you would calculate the sum of the first 20 terms as

With you would calculate

RELATED QUESTIONS
The term of an AP is 37 and the tenth term 53.Find sum of the twenty... (answered by ewatrrr)

The sixth term of an AP is 37 and the tenth term 53.Find the first... (answered by KMST)

sixth term of an AP. Is 37 and tenth term 53 and fine the common... (answered by ewatrrr)

The sum of the first and second term of an AP is 4,if the tenth term is 19 find the sum... (answered by richwmiller)

The first term of an Ap is-1 and the sum of the first twenty terms is -240 .find the... (answered by greenestamps)

In an AP consisting of 15 terms, the sum of the last five terms is 305. If the sixth term (answered by ikleyn)

Find the sum of the first 25 terms of an AP whose nth term is... (answered by stanbon)

Find the sum of first 15 terms of an AP., whose nth term is... (answered by mananth)

The twenty first term of an ap is five and a half while the sum of the twenty one terms... (answered by greenestamps)