Math, asked by krishnaveniakula6, 5 months ago

25. The first three terms of the sequence whose general
term is tn =(-1)^n / 3+n​

Answers

Answered by řåhûł
9

Given:

Sequence whose general term is tn =(-1)^n / 3+n

To Find:

First three terms

Solution:

ATQ

tn =(-1)^n / 3+n

We need to find t1 , t2 and t3

t1 =(-1)^1 / 3+1

t1 = -1/4

t2 =(-1)^2 / 3+2

t2 = 1/5

t3 =(-1)^3 / 3+3

t3 = -1/6

Hence, first three terms of the given sequence are -1/4 , 1/5 and -1/6 respectively.

Answered by Anonymous
198

Step-by-step explanation:

Given :

  • general term is tn =(-1)^n / 3+n

To Find :

  • The first three terms t1 , t2 ,t3

Solution :

First term :

 :   \implies \sf \:  \:  \:  \:  \:  \:  \: t _{n} =  \frac{ { - 1}^{n} }{3 +n }  \\  \\

Substitute all values :

 :   \implies \sf \:  \:  \:  \:  \:  \:  \: t _{1} =  \frac{ { - 1}^{1} }{3 + \: 1}  \\  \\  \\  :   \implies \sf \:  \:  \:  \:  \:  \:  \: t _{1} =  \frac{ - 1}{4}  \\  \\

Second term :

 :   \implies \sf \:  \:  \:  \:  \:  \:  \: t _{n} =  \frac{ { - 1}^{n} }{3 +n }  \\  \\

Substitute all values :

 :   \implies \sf \:  \:  \:  \:  \:  \:  \: t _{2} =  \frac{ { - 1}^{2} }{3 + \: 2}  \\  \\  \\  :   \implies \sf \:  \:  \:  \:  \:  \:  \: t _{2} = \frac{1}{5}

Third terms :

 :   \implies \sf \:  \:  \:  \:  \:  \:  \: t _{n} =  \frac{ { - 1}^{n} }{3 +n }  \\  \\

Substitute all values :

 :   \implies \sf \:  \:  \:  \:  \:  \:  \: t _{3} =  \frac{ { - 1}^{3} }{3 + \: 3 }  \\  \\  \\  :   \implies \sf \:  \:  \:  \:  \:  \:  \: t _{3} = \frac{ - 1}{6}

{ \dag}  \sf \:  \:  \:  \underline{Hence \: t _{1} =  \frac{ - 1}{4}  ,\: t _{2} =  \frac{1}{5},t _{3} =  \frac{ - 1}{6}} \\

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