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The 8th and the 10th term of a geometric sequence are – 21 and - 189 respectively. What is the 2nd term of the sequence?

 Dec 4, 2020
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Let the 8th term  =  ar^7      where  a   = 1st term  and r  is the common ratio between terms

Likewise the 10th  term =   ar^9

 

So

ar^9  = - 189    (1)

ar^7 =    -21      (2)

 

Divide    (1)  by  (2)      and we  have  that    r^2 = 9    if  terms are increasing negatives →   r  = 3

 

And 

a(3)^9  = -189

a  =  -189 / 3^9   =  -189/19683 =  - 7/729

 

Second term  =   (-7/729)  * 3  =   -21/729  = -7/243

 

If the terms alternate signs  then  r  = -3

So

a(-3)^9  = -189

a =  189/19683  =  7/729

 

And the second term becomes  (7/729)(-3)  =  -7/243   (exactly the same !!! ) 

 

 

 

cool cool cool    

 Dec 4, 2020

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