Write down the sequence whose nth term is(i) n2n (ii) 3n3+(−1)n. How many terms of the sequences are are less than zero?

Let tn=n2nPut n = 1, 2, 3, 4, ........ we gett1=12=2t2=24=2t3=38t4=416=4So the sequence is 2,2, 38,4,.......(ii) Let tn=3n3+(−1)nPut n = 1, 2, 3, 4......t1=33+(−1)=32t2=(3)23+(−1)2=94t3=(3)33+(−1)3=272t4=(3)43+(−1)4=814So the sequence is 32,94,272,814,....

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

Write down the sequence whose n^{th} term is (i) {2^{n}}{n}

Question

Write down the sequence whose $n^{t h}$ term is
(i) $\frac{2 ^{n}}{n}$ (ii) $\frac{3 + ( - 1 ) ^{n}}{3 ^{n}}$ . How many terms of the sequences are are less than zero?

Views: 722 students

Found 3 tutors discussing this question

Eleanor Discussed

Write down the sequence whose

n^{t h}

term is
(i)

\frac{2 ^{n}}{n}

(ii)

\frac{3 + ( - 1 ) ^{n}}{3 ^{n}}

. How many terms of the sequences are are less than zero?

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Let

t_{n} = \frac{2 ^{n}}{n}

Put n = 1, 2, 3, 4, ........ we get

t_{1} = \frac{2}{1} = 2

t_{2} = \frac{4}{2} = 2

t_{3} = \frac{8}{3}

t_{4} = \frac{16}{4} = 4

So the sequence is

2, 2, \frac{8}{3}, 4, .......

(ii) Let

t_{n} = \frac{3 + ( - 1 ) ^{n}}{3 ^{n}}

Put n = 1, 2, 3, 4......

t_{1} = \frac{3 + ( - 1 )}{3} = \frac{2}{3}

t_{2} = \frac{3 + ( - 1 ) ^{2}}{( 3 ) ^{2}} = \frac{4}{9}

t_{3} = \frac{3 + ( - 1 ) ^{3}}{( 3 ) ^{3}} = \frac{2}{27}

t_{4} = \frac{3 + ( - 1 ) ^{4}}{( 3 ) ^{4}} = \frac{4}{81}

So the sequence is

\frac{2}{3}, \frac{4}{9}, \frac{2}{27}, \frac{4}{81}, ....

Was this solution helpful?

150

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Write down the sequence whose $n^{t h}$ term is (i) $\frac{2 ^{n}}{n}$ (ii) $\frac{3 + ( - 1 ) ^{n}}{3 ^{n}}$ . How many terms of the sequences are are less than zero?
Answer Type	Text solution:1
Upvotes	150

Write down the sequence whose nth term is(i) n2n​ (ii) 3n3+(−1)n​. How many terms of the sequences are are less than zero?

Text solutionVerified

Practice questions from similar books

Write down the sequence whose $n^{t h}$ term is
(i) $\frac{2 ^{n}}{n}$ (ii) $\frac{3 + ( - 1 ) ^{n}}{3 ^{n}}$ . How many terms of the sequences are are less than zero?