SOLUTION: please help me solve this challenge question on arithmetic sequences: if the 9th term of an arithmetic sequence is 27 and the 25th term is 123 what is the first term of the sequenc

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Question 522593: please help me solve this challenge question on arithmetic sequences: if the 9th term of an arithmetic sequence is 27 and the 25th term is 123 what is the first term of the sequence
Answer by Maths68(1474) About Me  (Show Source):
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nth term formula of an arithmetic sequence = a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
a%5B9%5D=27
n=9
Substitute the values in nth term formula
27=a%5B1%5D%2B%289-1%29d
27=a%5B1%5D%2B8d....................(1)
and
a%5B25%5D=123
n=25
Substitute the values in nth term formula
123=a%5B1%5D%2B%2825-1%29d
123=a%5B1%5D%2B24d...................(2)
Subtract (1) from (2)
123=a%5B1%5D%2B24d
-27=-a%5B1%5D-8d
-----------------
96=16d
96%2F16=d
6=d
d=6
Plug in the value of d in (1)
27=a%5B1%5D%2B8d
27=a%5B1%5D%2B%288%2A6%29
27=a%5B1%5D%2B48
%2827-48%29=a%5B1%5D
-21=a%5B1%5D
a%5B1%5D=-21
First term of the given sequence is -21