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

Is it D?

Explanation: 1) we have the first term for the series. Rest is just calculating based on the given condition.

2) Take first expression as x, use the given condition to evaluate 5th and 6th term. We will have a linear equation to get the value of x.

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I think the answer would be E?

Using a linear equation of 2X + 1 = Y
Term 1: X = 1, Y = 3
Term 2: X = 3, Y = 7
Term 3: X = 7, Y = 15
Term 4: X = 15, Y = 31
Term 5: X = 31, Y = 63
Term 6: X = 63, Y = 127

127 - 63 = 64

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