Question

Given below are two statements
Statement I: In the sequence of numbers 30, 90, 182, 306, 462, P...... the term P is 650.
Statement II: There are 8 digits in 9⁸ when it is expressed in decimal form.
In light of the above statements, choose the correct answer from the options given below

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Answer 1

The Correct Option is A

To determine the correctness of the statements, let's analyze each statement independently: 

Statement I: In the sequence of numbers 30, 90, 182, 306, 462, P...... the term P is 650.

This sequence appears to follow the pattern of triangular numbers multiplied by 3. Triangular numbers are given by the formula:

\(T_n = \frac{n(n+1)}{2}\)

Multiplying these numbers by 3 gives us the sequence in the question:

n	Triangular Number	Sequence Element
5	15	30
9	45	90
13	91	182
17	153	306
21	231	462
25	325	650

Thus, \(P = 650\), confirming that Statement I is true.

Statement II: There are 8 digits in 9⁸ when it is expressed in decimal form.

To verify, calculate \(9^8\) and count the digits. Using: \(9^8 = 43046721\).

Counting the digits: \(43046721\) has 8 digits.

Therefore, Statement II is true.

Conclusion

Both Statement I and Statement II are true. Therefore, the correct answer is:

Both Statement I and Statement II are true