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 Question from Japheth, a student: The 3rd term of an A.P is 10 more than the first term while the fifth term is 15 more than the second term. Find the first term?

Japheth,

There is something missing here. In an A.P. the difference between any term and the next term is always the same. This is the common difference. To progress from the first term to the third term you have added the common difference twice and since the third term is 10 more than the first term the common difference is $\large \frac{10}{2} \normalsize = 5.$ To progress from the second term to the fifth term you add the common difference 3 times and hence the fifth term is $3 \times 5 = 15$ more than the second term. Thus the statement that "the fifth term is 15 more than the second term" doesn't tell you anything new. Was there some other information given? The way the problem is given there isn't enough information to determine the first term.

Penny

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