FINDING Nth TERM OF A GEOMETRIC SERIES

Write down formulae for the n^th term of these sequences :

Problem 1 :

3, 6, 12, 24, …

Problem 2 :

36, 18, 9, 4.5, …

Problem 3 :

2, -6, 18, -54, …

Problem 4 :

90, -30, 10, -3 1/3, …

Problem 5 :

10, 100, 1000, …

Problem 6 :

6, -6, 6, -6, …

Problem 7 :

1/4, 1/12, 1/36, 1/108, …

Answer Key

1) a_n = 3 ⋅ 2^{n - 1}

2) a_n = 36 ⋅ (1/2)^{n - 1}

3) a_n = 2 ⋅ (-3)^{n - 1}

4) a_n = 90 ⋅ (-1/3)^{n - 1}

5) a_n = 10 ⋅ (10)^{n - 1}

6) a_n = 6 ⋅ (-1)^{n - 1}

7) a_n = ((1/3)^{n – 1})/4