Question 1085451: The 18th and 52nd terms of an arithmetic sequence are 3and 173, respectively. Which term is 38?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if it's an arithmetic sequence, then there is a common difference between terms.
your 18th term is equal to 3 and your 52d term is equal to 173.
take 52 and subtract 18 to get 34
take 173 and subtract 3 to get 170
170 / 34 = 5
the common difference difference between one element and the next element is 5.
in order to go from 3 to 38, you have to add 35
35 / 5 is equal to 7
3 is the 18th term.
add 7 to that and you get 35 is the 18 + 7 = 25th term.
how do we know this is good?
you can create your sequence starting from 3 and working upwards 5 at a time, or, if you know the formula for an arithmetic sequence, you can use that.
the formula for an arithmetic sequence is An = A1 + (n-1) * d
An is the nth term.
A1 is the first term
n is then umber of terms
d is the common difference between terms.
you just solved for the common difference and you know at least one of the nth terms.
we'll take term number 18.
the formula of An = A1 + (n-1) * d becomes:
3 = A1 + (17 * 5)
solve for A1 to get A1 = 3 - (17 * 5) which becomes A1 = 3 - 85 which becomes A1 = -82
we now have A1 = -82 and d = 5
A18 = -82 + 17 * 5 = 3
A52 = -82 + 51 * 5 = 173
A25 = -82 + 24 * 5 = 38
everything checks out so we're good.
you didn't need the formula to solve this.
you just had to know that it was an arithmetic sequence which means there's a common difference between each element in the sequence.
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