SOLUTION: The ninth term of an arithmeticsequence is 42 and the sum of the fist term is 414. Find the first term of the sequence.

Question 845973: The ninth term of an arithmeticsequence is 42 and the sum of the fist term is 414. Find the first term of the sequence.
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
Let the first term of the AP be 'a' and the common difference be 'd'.
Therefore the n-th term is
The sum up to first n-terms is

Here, n=9,

9th term is given by

_______ (1)

Sum of first 9 terms is given by

_______ (2)

Subtracting both sides of equation (2) from (1)

Substituting in (2) we have

First term of the sequence is 50.
Cheers!!!
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