Get 2 FREE Instant-Explanations on Filo with code FILOAPP

m, 2m, 4m, . . . The first term in the sequence above is m, an

Question

$m, 2 m, 4 m, ...$
The first term in the sequence above is $m$ , and each term thereafter is equal to twice the previous term. If $m$ is an integer, which of the following could NOT be the sum of the first four terms of this sequence?

- 26

- 15

45

75

120

Views: 867 students

Found 4 tutors discussing this question

Camila Discussed

m, 2 m, 4 m, ...

The first term in the sequence above is

m

, and each term thereafter is equal to twice the previous term. If

m

is an integer, which of the following could NOT be the sum of the first four terms of this sequence?

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

The first term in given Geometric series,

a_{1} = m

The common ratio

r

= \frac{4 m}{2 m} = 2

No. of terms,

n

= 4

Applying sum of GP formula,

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

= \frac{m ( 1 - 2 ^{4} )}{1 - 2}

= \frac{m ( 1 - 16 )}{- 1} = 15 m

m

is an integer the sum of the first four terms of this sequence should be in multiple of

15

.
Hence, option A is correct which is not a multiple of

15

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

231 students are taking LIVE classes

Question Text	$m, 2 m, 4 m, ...$ The first term in the sequence above is $m$ , and each term thereafter is equal to twice the previous term. If $m$ is an integer, which of the following could NOT be the sum of the first four terms of this sequence?
Answer Type	Text solution:1
Upvotes	150