SUM OF A G.P 1

The sum of the 1st seven terms of a geometrical progression is 635. If the common ratio is 2 find the 1st term.

Solution

S₇ = 635 G₁ = ?, r=2, n=7

S_n = G₁(rⁿ-1)/r-1

             

S₇ = G₁(r⁷-1)/r-1

              

635= G₁(2⁷-1)/2-1

               

635= G₁(128-1)

                  1

635 = G₁(127)

                  

⁵635= 127G₁

 127   127

5 = G₁

G₁ = 5

Hence the 1st term is 5.

TRY THIS.........................................

The sum of the 1st seven terms of a geometrical progression is 635. If the common ratio is 2 find the 1st term.