38. In the sequence above, each term after the first term is found by subtracting 3 from twice the preceding term. What is the fifth term of the sequence?5,7,11….
Answer: C
The fifth term of the sequence is 35.
To find the fifth term of the sequence, we apply the rule of subtracting 3 from twice the preceding term. Starting with the first term, 5, we can calculate each subsequent term until we reach the fifth.
A) 19
Option A is incorrect as it does not satisfy the formula given. The calculation for the fourth term from the third term (11) would be 2*11 - 3 = 19, which is the fourth term, not the fifth.
B) 26
Option B is also incorrect. Following the same calculation, if we take 7 (the second term), the third term becomes 2*7 - 3 = 11, and the fourth term calculated from 11 is 19, leaving us with no basis for 26 as a fifth term.
C) 35
Option C is correct. Continuing from the fourth term, which we calculated as 19, the fifth term is found by taking 2*19 - 3 = 35. Thus, 35 is indeed the fifth term of the sequence.
D) 38
Option D is incorrect because, using the sequence rule, if we take the fourth term (19), the calculation for the fifth term yields 2*19 - 3 = 35, not 38.
E) 46
Option E is incorrect as well. The calculation for the fifth term does not support 46 since 2*19 - 3 = 35, which is far less than 46.
Conclusion
The correct answer is 35, as it directly follows from the sequence's defined rule. All other options fail to provide the correct fifth term based on the established formula, confirming that 35 is the only option that accurately represents the next term in the sequence.