SOLUTION: Given that A 5 = 46 and A7 = 60 are the 5th and 7th terms in a arithmetic sequence find

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Question 932491: Given that A 5 = 46 and A7 = 60 are the 5th and 7th terms in a arithmetic sequence find
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
system%28a%5B6%5D=a%5B5%5D%2Bd%2Ca%5B7%5D=a%5B6%5D%2Bd%29

system%28a%5B6%5D=46%2Bd%2C60=a%5B6%5D%2Bd%29

Use substitution of 46+d for a6 in 2nd equation

60=46%2Bd%2Bd
60=46%2B2d
14=2d
7=d

Then use formula

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d with n=5 and a5=46

a%5B5%5D=a%5B1%5D%2B%285-1%297

46=a%5B1%5D%2B%284%297
46=a%5B1%5D%2B28
18=a%5B1%5D

So 

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d becomes:

a%5Bn%5D=18%2B%28n-1%297

a%5Bn%5D=18%2B7%28n-1%29

a%5Bn%5D=18%2B7n-7

a%5Bn%5D=7n%2B11

You didn't say what you wanted to find but you can use
that formula to find any term.

Or you ccan find a formula to use for the sum of any
numer of terms:

S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29

S%5Bn%5D=expr%28n%2F2%29%282%2818%29%2B%28n-1%297%29

S%5Bn%5D=expr%28n%2F2%29%2836%5E%22%22%2B7%28n-1%29%29

S%5Bn%5D=expr%28n%2F2%29%2836%2B7n-7%29

S%5Bn%5D=expr%28n%2F2%29%287n%2B29%29

Edwin