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Question
Write the first five terms of the sequences whose nth term is:
`a_n = n (n^2 + 5)/4`
Solution
an = `"n"("n"^2 + 5)/4`
Substituting n = 1, 2, 3, 4, 5, we get
a1 = `1 (1^2 + 5)/4 = 6/4 = 3/2`,
a2 = `2 (2^2 + 5)/4 = (2 xx 9)/4 = 9/2`,
a3 = `3 (3^2 + 5)/4 = (3 xx 14)/4 = 21/2`,
a4 = `4 (4^2 + 5)/4 = (4 xx 21)/4` = 21,
a5 = `5 (5^2 + 5)/4 = (5 xx 30)/4 = 75/2`
Hence, the five terms of the sequence are `3/2, 9/2, 21/2, 21, 75/2`.
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