Tag: maths

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Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

A sum to $n$ terms of the series $\dfrac{3}{2^1 \cdot 2 \cdot 1} + \dfrac{4}{2^2 \cdot 3 \cdot 2} + \dfrac{5}{2^3 \cdot 4 \cdot 3} + \dfrac{6}{2^4 \cdot 5 \cdot 4} + ...$ is $S _n$ then

  1. $S _{10} = \dfrac{11263}{11264}$
  2. $S _{10} = \dfrac{22527}{11264}$
  3. If $n$ approaches $\infty, S _n$ approaches to $1$
  4. If $n$ approaches $\infty, S _n$ approaches to $2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

The average of certain first consecutive even number is $101$. Find their sum?

  1. $25,000$
  2. $33,600$
  3. $10100$
  4. $24,960$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The average of the first n consecutive even numbers (2, 4, 6, ..., 2n) is given by (2 + 2n)/2 = n + 1. We are given that the average is 101, so n + 1 = 101, which means n = 100. The sum of the first n consecutive even numbers is n(n + 1) = 100 * 101 = 10100.