GEOMETRIC PROGRESSION 4

Find the sum of the 1st eight terms of the geometrical progression 2+6+18+54+…….

solution

G₁ = 2, r=3, n=8

S_n = G₁(rⁿ-1)/r-1

               

S₈ = 2(3⁸-1)/3-1

             

S₈ = ¹2(3⁸-1)/2₁

              

S₈ = (3⁸-1)

S₇ = 6561 – 1               [Since  3⁸  =6561]

S₇ = 6560

Hence the sum of the 1st seven terms is 6560.

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Find the sum of the 1st six terms of the geometrical progression 5+10+20+40+…..