Tag: triangular numbers

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Questions Related to triangular numbers

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

If $\displaystyle { a }^{ 2 }$ ends in 5, then $\displaystyle { a }^{ 3 }$ ends in 25.

  1. True

  2. False

  3. Ambiguous

  4. Insufficient information
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

False. 15 x 15=225 and 15 x 15 x 15=3375. so the statement $\displaystyle { a }^{ 2 }$ ends in 5, then $\displaystyle { a }^{ 3 }$ ends in 25 is not true in all cases.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

If $\displaystyle n = 1 + x $, where $x$ is the product of four consecutive positive integers then which of the following is/are true:
A) n is odd

B) n is prime
C) n is a perfect square

  1. A and C only

  2. A and B only

  3. A only

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let us take $\displaystyle x=1\times2\times3\times4=24 $

Then $\displaystyle n=1+24=25$
i.e. an odd number and a perfect square
Again let $\displaystyle x=2\times3\times4\times5=120.$
Then, $\displaystyle n=1+120=121$
i.e. an odd number and a perfect square
$\displaystyle \therefore $ Option (A) is correct