SOLUTION: Please help me with this problem Write a rule for the nth term of the arithmetic sequence where 𝑎4 = 14 and 𝑎10 = 47

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Question 1201664: Please help me with this problem

Write a rule for the nth term of the arithmetic sequence where
𝑎4 = 14 and 𝑎10 = 47
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Find how many common differences are from term number 4 to term number 10.
How much is 47 minus 14?
Do you see, and can you complete the rest on your own?

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Please help me with this problem
Write a rule for the nth term of the arithmetic sequence where
𝑎4 = 14 and 𝑎10 = 47
~~~~~~~~~~~~~~~~~~~~~~ 

Write formulas for the 4th and 10th terms

    a4  = a1 + 3d = 14     (1)
    a10 = a1 + 9d = 47     (2)


Subtract (1) from (2)

    9d - 3d = 47 - 14

       6d   =    33

        d   =    33/6 = 5.5.


Half of the problem is just solved.


Now from equation (1), 

    a1 = 14 - 3*d = 14 -3*5.5 = 14 - 16.5 = -2.5.


Thus the first term of the AP is -2.5;  the common difference is d= 5.5.


Hence, the formula for the n-th term is

    a%5Bn%5D = -2.5 + (n-1)*5.5 = -2.5 + 5.5n - 5.5 = -8 + 5.5n.    ANSWER

Solved.