Q. 14.7( 3 Votes )

# Write the first three terms of the following sequences whose n^{th} terms are given by

(i) (ii) c_{n} = (–1)^{n}3^{n+2} (iii)

Answer :

(i) Here, a_{n} =

For n = 1, a_{1} = = =

For n = 2, a_{2} = = = = 0

For n = 3, a_{3} = = = = 1

Hence, the first three terms of the sequence are, 0 and 1.

(ii) Here, c_{n} = (-1)^{n} 3^{n + 2}

For n = 1, c_{1} = (-1)^{1} 3^{1 + 2} = (-1) 3^{3} = (-1) (27) = -27

For n = 2, c_{2} = (-1)^{2} 3^{2 + 2} = (1) 3^{4} = (1) (81) = 81

For n = 3, c_{3} = (-1)^{3} 3^{3 + 2} = (-1) 3^{5} = (-1) (243) = -243

Hence, the first three terms of the sequence are -27, 81 and -243.

(iii) Here, z_{n} =

For n = 1, z_{1} = = =

For n = 2, z_{2} = = = = 2

For n = 3, z_{3} = = =

Hence, the first three terms of the sequence are, 2 and.

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