Multiple choice

What is the difference between the sixth and the fifth terms of the sequence $2, 4, 7, ...$ whose $n^{th}$ term is $\displaystyle n+2^{ n-1 }$ ?

  1. $2$
  2. $3$
  3. $6$
  4. $16$
  5. $17$
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E Correct answer
Explanation

n-th term = n + 2^(n-1). 5th term = 5 + 2^4 = 5 + 16 = 21. 6th term = 6 + 2^5 = 6 + 32 = 38. Difference = 38 - 21 = 17.

AI explanation

Using the provided formula for the nth term, n + 2^(n - 1), we first find the fifth term by substituting n = 5 to get 5 + 2^4 = 21. Next, we find the sixth term by substituting n = 6 to get 6 + 2^5 = 38. The difference between the sixth and fifth terms is 38 - 21 = 17.

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