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Sequence next term and digits in 9^8 statements

CMAT 2021 · Quantitative Techniques & Data Interpretation · Medium · Sequences and Series

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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 989^8 when it is expressed in decimal form.

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

  1. A.

    Both Statement I and Statement II are true

  2. B.

    Both Statement I and Statement II are false

  3. C.

    Statement I is true but Statement II is false

  4. D.

    Statement I is false but Statement II is true

Answer

A

Explanation

Statement I: Differences between consecutive terms:

  • 90−30=6090 - 30 = 60
  • 182−90=92182 - 90 = 92 (diff increase = 32)
  • 306−182=124306 - 182 = 124 (diff increase = 32)
  • 462−306=156462 - 306 = 156 (diff increase = 32)

Next difference = 156+32=188156 + 32 = 188. So P=462+188=650P = 462 + 188 = 650. Statement I is true.

Statement II: Number of digits in 98=⌊8log⁡109⌋+1=⌊8×0.9542⌋+1=⌊7.6336⌋+1=7+1=89^8 = \lfloor 8 \log_{10} 9 \rfloor + 1 = \lfloor 8 \times 0.9542 \rfloor + 1 = \lfloor 7.6336 \rfloor + 1 = 7 + 1 = 8. Statement II is true.

Both statements are true.

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