SOLUTION: find the 25th term of the arithmetic sequence:26, 13, 0, -13

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Question 942808: find the 25th term of the arithmetic sequence:26, 13, 0, -13
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Each successive term is 13 less than the previous.
a%5Bn%5D=26-13%28n-1%29
a%5Bn%5D=26-13n%2B13
a%5Bn%5D=39-13n
So then when n=25
a%5B25%5D=39-13%2825%29
a%5B25%5D=39-325
a%5B25%5D=-286

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the 25th term of the arithmetic sequence:26, 13,+0,+-13.....


the nth term of the arithmetic sequence: a%5Bn%5D=a%5B1%5D+%2B%28n-1%29d where n is number of the term and d is common difference
you have the arithmetic sequence: 26, 13, 0,+-13 where a%5B1%5D=26 and a%5B2%5D=13, so the difference d=-13
a%5Bn%5D=a%5B1%5D+%2B%28n-1%29%28-13%29...check the third term ( or n=3)
a%5B3%5D=26+%2B%283-1%29%28-13%29
a%5B3%5D=26+%2B%282%29%28-13%29
a%5B3%5D=26+-26
a%5B3%5D=0 which is true
so, the 25th term will be:
a%5Bn%5D=a%5B1%5D+%2B%28n-1%29%28-13%29......plug in n=25 and a%5B1%5D=26
a%5B25%5D=26%2B%2825-1%29%28-13%29
a%5B25%5D=26%2B%2824%29%28-13%29
a%5B25%5D=26-312
a%5B25%5D=-286