Question

1, 7, 49, 343, (?)
a) 16807
b) 1227
c) 2058
d) 2401
e) None of these

Answer 1

Hey MATE!

These numbers are going in the series :
1, 7 , 49 , 343
${7}^{0} \\ {7}^{1} \\ {7}^{2} \\ {7}^{3}$
So the next number surely is

${7}^{4} = 2401$


Hope it helps

Hakuna Matata :))

Answer 2

Given,

We are given a series 1,7,49,343,

To find,

Find the next term of the series.

Solution,

• The above series is in Geometric Progression.

• A geometric progression is a progression in which each term is obtained by dividing or multiplying the preceding term by a fixed number also known as r.

• The general form of a Geometric Progression is ⇒a, ar, ar², ar³, and so on where a is the first term and r is the common term.

1, 7, 49, 343

In the above GP,

⇒   a = 1

⇒   (a)r = 7

⇒   r = 7.

• Now, we have found the common term of the GP that is r =7.

• Further solving,

⇒   1, 1(7), 1(7²), 1(7³), is in the form of a, ar, ar²,ar³

⇒   Therefore, the next term is $a(r)^{4}$

⇒   1($7^{4}$) = 2401

Hence, the next term of the series 1, 7, 49, 343 is 2401. (Option D)