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 $9^8$ when it is expressed in decimal form.

In light of the above statements, choose the correct answer from the options given below

Accepted Answer

A. Statement I: Differences between consecutive terms: - $90 - 30 = 60$ - $182 - 90 = 92$ (diff increase = 32) - $306 - 182 = 124$ (diff increase = 32) - $462 - 306 = 156$ (diff increase = 32) Next difference = $156 + 32 = 188$. So $P = 462 + 188 = 650$. Statement I is true. Statement II: Number of digits in $9^8 = \lfloor 8 \log_{10} 9 floor + 1 = \lfloor 8 	imes 0.9542 floor + 1 = \lfloor 7.6336 floor + 1 = 7 + 1 = 8$. Statement II is true. Both statements are true.

Sequence next term and digits in 9^8 statements

Explanation

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