Question 1201664
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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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<pre>
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[n]}}} = -2.5 + (n-1)*5.5 = -2.5 + 5.5n - 5.5 = -8 + 5.5n.    <U>ANSWER</U>
</pre>

Solved.