Question

Find the nth term in the sequence: 0, 1/2, 3/4, 7/8, 15/16, 31/32...

A) 1 - (1/2)^n
B) 1/2^n
C) 1 + (1/2)^n
D) 1 - (1/2)^(n-1)
E) None of the above.

Answer 1

The correct formula for the nth term in the given sequence is A) 1 - (1/2) ^n, obtained by looking at the pattern where the numerator is one less than the power of 2 for the corresponding denominator.

Step-by-step explanation:

The sequence provided is 0, 1/2, 3/4, 7/8, 15/16, 31/32 and the student is asked to find the nth term in the sequence. On observing the pattern, we see that each term is obtained by subtracting a fraction from 1, with the denominator being a power of 2 and the power increasing by 1 with each subsequent term. To verify which option fits this pattern for any term 'n', we can see that each numerator is one less than the power of 2 for the corresponding denominator. Therefore, we can represent the numerator as 2^n - 1, making the nth term in the sequence (2^n - 1)/(2^n), which simplifies to 1 - (1/2) ^n. Thus, the correct formula is A) 1 - (1/2) ^n.