SOLUTION: The first and last terms of an AP are 67 and 171 respectively. If The first and last terms of an AP are 67 and 171 respectively. If there are 14 terms, find the 16th term of the A

Question 846928: The first and last terms of an AP are 67 and 171 respectively. If
The first and last terms of an AP are 67 and 171 respectively. If there are 14 terms, find the 16th term of the AP
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your solution is in the attached picture.
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the steps involved are shown below:

step 1 shows the original information you were provided with.

step 2 shows the arithmetic series formula.
a1 is the first term.
an is the nth term.
d is the common difference
n is the number of terms.

step 3 shows this formula replacing the letters with the information you were given.

step 4 subtracts 67 from both sides of the equation and step 5 shows the result of that operation.

step 6 divides both sides of the equation by 13 and step 7 shows the result of that operation.

step 8 uses the equation shown in step 2 and replaces n with 16 and d with 8 and a1 with 67.

step 9 simplifies the equation in step 8.

step 10 shows the result of the operation in step 9.
your solution is that the 16th term is equal to 187.

if the 14th term is equal to 171, and you add 8 to that, then you get 179 for the 15th term, and you add 8 to that, then you get 187 for the 16th term.

the results are confirmed to be reasonable.
your answer is that the 16th term is equal to 187.

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