SOLUTION: The 12th 85th and last terms of an arithmetic progression are 38 257 and 395 respectively. Find the number of term.

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Question 1070095: The 12th 85th and last terms of an arithmetic progression are 38 257 and 395 respectively. Find the number of term.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
a%5B12%5D=a%5B1%5D%2B%2812-1%29d=38
a%5B1%5D%2B11d=38
.
.
a%5B1%5D%2B84d=257
Subtracting the first equation from this equation,
a%5B1%5D%2B84d-a%5B1%5D-11d=257-38
73d=219
d=3
Then,
a%5B1%5D%2B11%283%29=38
a%5B1%5D%2B33=38
a%5B1%5D=5
So then,
a%5B1%5D%2B%28k-1%29d=395
Find k.
5%2B%28k-1%293=395
%28k-1%293=390
k-1=130
k=131
131 terms