Find the sum of the first 3 terms of a geometric sequence with a= 99 and r= - 4/3

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Aleah Harrell · Accepted Answer

A geometric sequence is a sequence of the form   a  ,  a  r  ,  a      r    2    ,  a      r    3    ,  a      r    4   ,..The number a is the first term, and r is the common ratio of thesequence. The nth term of a geometric sequence is given by       a          n        =  a      r          n      −      1      For the geometric sequence       a          n        =  a      r          n      −      1      , the nth partial sum      S          n        =  a  +  a  r  +  a      r          2        +  a      r          3        +  a      r          4        +  .  .  .  +  a      r          n      −      1        (  r  ≠  1  )     i  s     g  i  v  e  n     b  y         S          n        =  a            1      −              r                  n                            1      −      r      So the sum of the first 3 terms of a geometric sequence with a=99 and   r  =  −      4    3   is:      S          3        =  99  ∗            1      −      (      −              4        3                    )                  3                            1      −      (      −              4        3            )        =  99  ∗            91              /            27              7              /            3        =  99  ∗      13    9    =  143

tophergopher3wo · Accepted Answer

Thus, the general form of a geometric sequence is  a  ,  a  r  ,  a      r    2    ,  a      r    3    ,  a      r    4   ,...and that of a geometric series is  a  +  a  r  +  a      r    2    +  a      r    3    +  a      r    4  where   r  ≠  0 is the common ratio and ais a scale factor, equal to the sequence&#039;s start value.a=99,  r  =            −      4        3    a  +  a  r  +  a      r    2    +  a      r    3    +  a      r    4  first three term  99  +  99  ∗  (  −      4    3    )  +  99  (  −      4    3        )          2        =  99  (  1  −      4    3    +      16    9    )  =  143

Find the sum of the first 3 terms of a geometric sequence with a= 99 and r= - 4/3

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