SOLUTION: the third term of an A.P is 16 and its 6th term is 34 .find a:the common difference b:the first

Question 1084122: the third term of an A.P is 16 and its 6th term is 34 .find a:the common difference b:the first term c:the 20th term d:the sum of the first and 20 terms

Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.

 =  = 16,   (1)

 =  = 34.   (2)


====>  3d = 34 - 16 = 18  ====>  d =  = 6.


Then  =  = 16 - 2*6 = 4.


Then  =  = 4 + 19*6 = 118.


Then the sum of the first 20 terms is

 = . = . = 1220.

Solved.

There is a bunch of lessons on arithmetic progressions in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".

RELATED QUESTIONS
If the 4 th term of a AP is 16 and the 8 th term is 28 Find:- a) the first term b)... (answered by ikleyn,TeachMath)

If the 4 th term of a AP is 16 and the 8 th term is 28 Find:- a) the first term b)... (answered by ikleyn)

if the 6th term of an A.P is 35 and the 13th term is 27, calcuate the 20th... (answered by greenestamps)

5th term of an A.P is 9 and the 8th term is 27 find the 6th term and common difference... (answered by ikleyn)

the first term of an arithmetic sequence (AS) is 7 and the common difference is 3 find... (answered by ikleyn)

Given that the first term of an Arithmetical Progression is 7 and its 10th term is twice... (answered by mananth)

the 2nd and 6th terms are 1 and 27.find (a)the first term (b)common difference (c)10th... (answered by ewatrrr)

Thr 20th term of an arithmetic progression is 10 and the 50th term is 70, find the first... (answered by ikleyn)

Find the first term and the common difference of an arithmetic sequence if its 5th term... (answered by Edwin McCravy)