In a sequence of numbers in which each term after the first term is 1

The answer is D.

(1) give you the first term, so you can calculate the fifth term easily.
(2) we know that the sixth term is 1 more than twice the fifth, and its difference is 32. Call the fifth value is x, the difference can be formulated as 2x + 1 - x = x + 1 = 32 => x = 31

In a sequence of numbers in which each term after the first term is 1 more than twice the preceding term, what is the fifth term?

Yep. It's D.
We know that \(X_n = 2 X_{n-1} + 1\)


(1) The first term is 1.
Using the given from above, we can solve what \(x_5 = ?\)
\(x_0 = 1\)
You can work you're way up from there.

(2) The sixth term minus the fifth term is 32.
We know that
\(x_6 - x_5 = 32\)
\(x_6 = 2* x_5 + 1\)
\(2*x_5 + 1 - x_5 = 32\)
\(x_5 = 31\)

Given: In a sequence of numbers in which each term after the first term is 1 more than twice the preceding term
Let's take a moment to see what this pattern looks like.
Let k = the term_1
So, we get:
term_1 = k
term_2 = 2k + 1
term_3 = 2(k + 1) + 1 = 2k + 3
term_4 = 2(2k + 3) + 1 = 4k + 7
term_5 = 2(4k + 7) + 1 = 8k + 15
term_6 = 2(8k + 15) + 1 = 16k + 31

So, term_5 = 8k + 15

Target question: What is term_5?

Statement 1: The first term is 1.
In other words, k = 1
Since we already determined that term_5 = 8k + 15, we can substitute to get: term_5 = 8(1) + 15 = 16 + 15 = 31
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The sixth term minus the fifth term is 32
From our pattern we can see that term_5 = 8k + 15 and term_6 = 16k + 31
So, statement 2 is telling us that (16k + 31) - (8k + 15) = 32
Simplify the left side to get: 8k + 16 = 32
At this point, we can see that we COULD solve the equation for k, which means we COULD determine the value of term_5 the same way we did for statement 1 (although we would never waste valuable time on test day doing so)
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent