A sequence of numbers u_1, u_2, …, u_n, … is given by the formula $\displaystyle u_n = 3(\frac{2}{3})^n - 1 $ where n is a positive integer.

(a) Find the value of u_1, u_2 and u_3.

(b) Show that $\displaystyle \sum_{n=1}^{15} u_n = -9.014$ to 4 s.f.

(c) Proved that $\displaystyle u_{n+1} = 2 (\frac{2}{3})^3 - 1$.

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(a) u_1 = 1, u_2 = 1/3 & u_3 = -1/9.

How could I do rest of them?