How many terms of the G.P. 3, 23,43,˙˙˙are needed to give the sum 5123069?

Solution: Here, a=3andr=21Sn=1−ra(1−rn)5123069=1−(21)3(1−(21)n)10241023=1−(21)n(21)n=10241=(21)10So, n=10 is the required answer.

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

How many terms of the G.P. 3, {{3}}{{2}},{{3}}{{4}},{{{}}}are

Question

How many terms of the G.P. 3, $\frac{3}{2}$ , $\frac{3}{4}$ $, \dot{\dot{˙}}$ are needed to give the sum $\frac{3069}{512}$ ?

Views: 838 students

Found 2 tutors discussing this question

Mila Discussed

How many terms of the G.P. 3,

\frac{3}{2}

\frac{3}{4}

, \dot{\dot{˙}}

are needed to give the sum

\frac{3069}{512}

12 mins ago

Discuss this question LIVE

12 mins ago

Solution: Here,

a = 3 and r = \frac{1}{2}

S_{n} = \frac{a ( 1 - r ^{n} )}{1 - r}

\frac{3069}{512} = \frac{3 ( 1 - ( \frac{1}{2} ) ^{n} )}{1 - ( \frac{1}{2} )}

\frac{1023}{1024} = 1 - (\frac{1}{2})^{n}

(\frac{1}{2})^{n} = \frac{1}{1024} = (\frac{1}{2})^{10}

So,

n = 10

is the required answer.

Was this solution helpful?

150

Report

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 math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	How many terms of the G.P. 3, $\frac{3}{2}$ , $\frac{3}{4}$ $, \dot{\dot{˙}}$ are needed to give the sum $\frac{3069}{512}$ ?
Answer Type	Text solution:1
Upvotes	150