CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Method of Difference

There is a ce...

Question

There is a certain sequence of positive real numbers. Beginning from the third term, each term of the sequence is the sum of all the previous terms. The seventh term is equal to 1000 and the first term is equal to 1. The second term of this sequence is equal to

A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
sequence is $t_{1} + t_{2} + t_{3} + t_{4} + . . . . .$
$t_{3} = t_{1} + t_{2}; t_{7} = 1000$
$t_{1} = 1$
but $t_{7} = t_{1} + t_{2} + t_{3} + t_{4} + t_{5} + t_{6}$
$1000 = 2 (t_{1} + t_{2} + t_{3} + t_{4} + t_{5})$
$= 4 (t_{1} + t_{2} + t_{3} + t_{4})$
$= 8 (t_{1} + t_{2} + t_{3})$
$1000 = 16 (t_{1} + t_{2})$
$t_{1} + t_{2} = ∋ t_{2} = - 1 = - 1 =$

Suggest Corrections

thumbs-up

5

Similar questions

x, 2 x, 4 x, . . .

The first term in the sequence above is

x

, and each term thereafter is equal to twice the previous term. Find the sum of the first five terms of this sequence.

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?

a, 2 a - 1, 3 a - 2, 4 a - 3, . . .

For a particular number

a

, the first term in the sequence above is equal to

a

and each term thereafter is

7

greater than the previous term. What is the value of the

16 t h

term in the sequence?

Q. The first term in a sequence is 1 and the second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 25th term in the sequence?

Q. After the first term in a sequence of positive integers, the ratio of each term to the term immediately preceding it is

2

1

. What is the ratio of the

8^{t h}

term in this sequence to the

5^{t h}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Method of Difference

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Method of Difference

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon