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# Sum of a Sequence

ACTMAT-PS1ETV

If S represents the sum of the first 6 terms of the sequence:

$$a+b, 2a+{ b }^{ 2 }, 3a+{ b }^{ 3 },...$$

...then which of the following is S?

A

$21a+\cfrac { b-{ b }^{ 7 } }{ 1-b }$

B

$21a+\cfrac { 1-{ b }^{ 8 } }{ 1+b }$

C

$21a+\cfrac { b-{ b }^{ 8 } }{ 1-b }$

D

$28a+\cfrac { 1-{ b }^{ 7 } }{ 1-b }$

E

$21a+\cfrac { b-{ b }^{ 8 } }{ 1+b }$