SOLUTION: If the 4 th term of a AP is 16 and the 8 th term is 28 Find:- a) the first term b) the common difference c) The 16th term

Question 1109076: If the 4
th term of a AP is 16 and the 8
th term is 28
Find:- a) the first term
b) the common difference
c) The 16th term
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.

the 4-th term is   =  = 16    (1)

the 8-th term is   =  = 28.   (2)



Subtract eq(1) from eq(2). You will get


    7d - 3d = 28 - 16 = 12  ====>  4d = 12  ====>  d =  = 3.


Thus you just found the common difference d. It is 3.



Next, from eq(1)   = 16 - 3d = 16 - 3*3 = 7.

Thus, the first term   = 7.


Then the 16-term is   =  = 7 + 15*3 = 52.

I answered all your questions.

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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".

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Free of charge online textbook in ALGEBRA-II
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