Question

Determine the formula for the calculation of sum of n terms in a geometric progression (G.P)?

 

Answer 1

Determine the formula for the calculation of sum of n terms in an geometric progression (G.P)?

Sol. 

For a G.P,

Sum, Sn = a + a^r + ar² + ........  ar^n-3 + ar^n-2 +ar^n-1        - I

Multiplying b/s by r

Sum, Sn = a^r + ar² + ar³ +....... + ar^n-2 +ar^n-1 + arⁿ           - II

To calculate the sum of n terms in the geometric progression we subtract II from I or I from II and proceed as follows:

Sum, Sn = a(1 - rⁿ)/(1 - r); When |r| < 1

Sum, Sn = a(rⁿ- 1)/( r - 1 ); When |r| > 1

Sum, Sn is undefined; When |r| = 1

Sum, Sn = a(1 - rⁿ)/(1 - r); When |r| < 1

Sum, Sn = a(rⁿ- 1)/( r - 1 ); When |r| > 1

Sum, Sn is undefined; When |r| = 1