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Question
Write the nth term of the following sequences.
6, 10, 4, 12, 2, 14, 0, 16, −2, . . .
Solution
The given sequence is 6, 10, 4, 12, 2, 14, 0, 16, – 2 …
The odd terms are a1 = 6,
a3 = 4,
a5 = 2,
a7 = 0,
a9 = – 2
∴ an = 7 - n
= 7 - 1 = 6
= 7 - 3 = 4
= 7 - 5 = 2
7 - n, if n is odd
The even terms are a2 = 10,
a4 = 12,
a6 = 14,
a8 = 16
∴ an = 8 + n, n is even.
∴ an = `{{:("n" - 7, "if n is odd"),(8 + "n", "if n is even"):}`
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