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# The problem is this "Find the first term of the series with an=324, r=3, Sn=484" I have no idea where to start please help!

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The problem is this "Find the first term of the series with an=324, r=3, Sn=484" I have no idea where to start please help!

Guest Mar 26, 2017
#1
+87604
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The sum, Sn,  of the first n terms of a geometric series =

Sn  = a1  ( 1 - r^n) / ( 1  - r)   where a1 is the first term and r is the common ratio

484  = a1  ( 1 - 3^n)  / (1 -3)

484  =  a1 ( 1 - 3^n) / -2

-968  = a1 ( 1 - 3^n)      rearrange  as

a1  =   -968 / ( 1 - 3^n)    factor out a negative

a1  =  968 /(3^n - 1)         (1)

And  the nth term is given by

an  = a1 (3)^(n -1)

324  = a1 * (3)^(n - 1)       sub (1)  into this for  a1

324  = 968 / (3^n - 1) * 3^(n - 1)         .......3^(n - 1)   =  3^n / 3

324 (3^n - 1)  =  968  (3^n) / 3

972 (3^n - 1)  = 968 (3^n)

972 (3^n)  - 972   = 968 (3^n)

972(3^n) - 968(3^n)  =  972

4(3^n)  = 972

3^n  =  243        ..........243  = 3^5

3^n  = 3^5

So.....n = 5

So....using (1)

The first term, a1  =

968 / (3^n - 1)

968/ ( 3^5 - 1)

968 / (243 - 1)

968 / 242 =

4

CPhill  Mar 26, 2017
edited by CPhill  Mar 26, 2017