SOLUTION: Two terms of an arithmetic sequence are a8 =76 and a28=96 find a rule for the nth term

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Question 294448: Two terms of an arithmetic sequence are a8 =76 and a28=96 find a rule for the nth term
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
In general,
an=a1%2Bn%2Ad
Find a1 and d,
1.a8=a1%2B8%2Ad=76
2.a28=a1%2B28%2Ad=96
From eq. 1,
a1=76-8%2Ad
Substitute into eq. 2,
a1%2B28%2Ad=96
%2876-8%2Ad%29%2B28%2Ad=96
76%2B20%2Ad=96
20%2Ad=20
d=1
Then from eq. 1,
a1=76-8%2Ad
a1=76-8%2A1
a1=76-8
a1=68
So then the rule becomes,
an=68%2B1%28n%29
an=68%2Bn