Find the indicated terms in the following sequence whose nth ter

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 Multiple Choice QuestionsShort Answer Type

1.

Write the first five terms of each of the sequences whose nth terms are :

straight a subscript straight n space equals space fraction numerator straight n left parenthesis straight n squared plus 5 right parenthesis over denominator 4 end fraction

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2.

Write the first five terms of the sequence whose nth terms are:

straight a subscript straight n space equals space left parenthesis negative 1 right parenthesis to the power of straight n minus 1 end exponent space 5 to the power of straight n plus 1 end exponent







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3.

Find the indicated terms in the following sequence whose nth terms are :

space space straight a subscript straight n space equals space fraction numerator straight n left parenthesis straight n minus 2 right parenthesis over denominator straight n plus 3 end fraction


Here, straight a subscript straight n space equals space fraction numerator straight n left parenthesis straight n minus 2 right parenthesis over denominator straight n plus 3 end fraction semicolon space space straight a subscript 19

Putting n = 19, we get straight a subscript 19 space equals space fraction numerator 19 left parenthesis 9 minus 2 right parenthesis over denominator 19 plus 3 end fraction space equals space fraction numerator 19 cross times 17 over denominator 22 end fraction equals 323 over 22

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4.

Find the indicated terms in the following sequence whose nth terms are:

straight h left parenthesis straight n right parenthesis space equals space fraction numerator straight n squared plus 2 straight n over denominator 2 straight n end fraction semicolon space straight h left parenthesis straight n minus 1 right parenthesis comma space straight h left parenthesis 16 right parenthesis


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5.

The Fibonacci sequence is defined by

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Find fraction numerator straight a subscript straight n plus 1 over denominator straight a subscript straight n end fraction, for n = 1, 2, 3, 4, 5.


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6.

Find the first six terms of the sequence whose first term is 1 and whose (n+l)th term is obtained by adding n to the nth term.

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 Multiple Choice QuestionsLong Answer Type

7.

Consider the sequence defined by tn = an2 + bn + c. If t2 = 3, t4 = 13 and t7 = 113, show that 3tn = 17n2 – 87n + 115

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 Multiple Choice QuestionsShort Answer Type

8.

Write first five terms of the following sequence and obtain the corresponding series.

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#6 {main}</pre> for all n>1

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9.

Write first five terms of the following sequence and obtain the corresponding series.

straight a subscript 1 space equals space straight a subscript 2 space equals space 2 comma space space space straight a subscript straight n space equals space straight a subscript straight n minus 1 end subscript space minus space 1, n>2

211 Views

10.

Show that the sequence space space open curly brackets straight t subscript straight n close curly brackets defined by straight t subscript straight n space equals space nA space plus space straight B (where A and B are constant) is an A.P. with common difference A.

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