Question 1020019: Please help me solve these question, in geometric progression. The first and the last term of the geometric progression are 2 and 2,048 respectively.The sum of the term of the progression is 2,730 find the number of terms and the common ratio (c.r)
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! The first term  , the nth term is  = 2,048.
The sum of the first n terms of a geometric sequence is given by the formula
After substitution,
<==> 2730 - 2730r = 2 - 2,048r, after cross-multiplying.
<==> 2,728 = 682r
<==>  , the common ratio (c.r.)
Now from the formula for the nth term of a gp,  ,
we get
 , and we proceed to determine the value of n.
<==> 
==> 
==> 10 = 2n - 2
==> 12 = 2n
==>  , the number of terms added in the sequence,
and the problem is solved.
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