Question 1085451
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.