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Example: Find the formula for n^{th} term in the sequence: 2, 5, 8, 11, 14, . . . This is an arithmetic sequence d = 3 a_{1} = 2 a_{n} = 2 + (n  1)3 Therefore : The n^{th}th term for the sequence is a_{n} = 3n 1 Verify: By putting in 1, 2, 3, ...... and you get the sequence Example: Find the formula for n^{th} term in the sequence: 2, 4, 8, 16, 32, . . . This is geometric sequence. a_{1} = 2 r = 2 Therefore, a_{n} = 2 . 2^{(n  1)} a_{n} = 2.2^{n1} Verify: By putting in 1, 2, 3, ........and see if you get the sequence Example: Find the formula for nth term in the sequence: 21, 201, 2001, 20001, . . . This is neither geometric or arithmetic. Think of the sequence as (20 +1), (200+1), (2000 + 1), (20000 + 1), . . . It can be written as the sequence:[(2)(10) +1],[(2)(100) +1], [(2)(1000) +1], [(2)(10000) +1] Check and see a pattern with powers of 10 a_{n} = 2.10^{n} + 1
Example: More examples:
Directions: Find the formula for the nth term in the sequence. Also write at least 5 examples of your own. 