Question

Find the 14th term in the sequence 1, 1/3, 1/9, … Find the sum of the first 10 terms of the sequence above.

Answer 1

This is a geometric progresion that begins with 1 and each term is 1/3 the preceeding term

Let Pn represent the nth term in the sequence

Then Pn = (1/3)^n-1

From this P14 = (1/3)^13 = 1/1594323

5. The sum of the first n terms of a GP beginning a with ratio r is given by

Sn = a* (r^n+1 - 1)/(r - 1)

With n = 10, a = 1 and r = 1/3, S10 = ((1/3)^11 - 1)/(1/3 - 1) = 1.500