+0  
 
0
467
3
avatar+14 

The third term of a Geometric Sequence is 27 and the fifth term is 243. What is the sum of the first 10 terms?

Matimatix  Jul 4, 2017
 #1
avatar+9515 
+2

31 =3

32 = 9

33 = 27

34 = 81

35 = 243

36 = 729

37 = 2187

38 = 6561

39 = 19683

310 = 59049

         88572

\({s}_{n} = \frac{q^n-1}{q-1}*{a}_{1}\)

 

q=3   n=10

 

laugh

Omi67  Jul 4, 2017
 #2
avatar+87537 
+2

 

The common ratio  is given by :

 

243 / 27  =  r^2

 

9  =  r^2    →   3  = r

 

And the first term  is

 

27 / 3^2  =   27/9 = 3

 

And the sum ofr the first 10  terms  is given by :

 

first term  [ 1 - common ratio^10] / [1 - common ratio ]  =

 

3 [ 1 - 3^10] / [ 1 - 3 ]  = 88572

 

 

cool cool cool

CPhill  Jul 5, 2017
 #3
avatar+14 
0

can you tell me the complete solution? My teacher needs it.

Matimatix  Jul 5, 2017

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