To find the pattern in the given sequence: 2, 5, 17, 65, _______, 1025, we need to look for the relationship between the terms.
If we observe carefully, we can see that each term in the sequence is obtained by multiplying the previous term by 3 and then adding 1.
Let's go through each option to determine the correct answer:
Option A) 256 - This option does not follow the pattern of multiplying the previous term by 3 and adding 1.
Option B) 258 - This option does not follow the pattern of multiplying the previous term by 3 and adding 1.
Option C) 257 - This option is correct because it follows the pattern of multiplying the previous term by 3 and adding 1. For example, 65 x 3 + 1 = 196 + 1 = 197.
Option D) 259 - This option does not follow the pattern of multiplying the previous term by 3 and adding 1.
Option E) 260 - This option does not follow the pattern of multiplying the previous term by 3 and adding 1.
Option F) 261 - This option does not follow the pattern of multiplying the previous term by 3 and adding 1.
The correct answer is Option C) 257. This option is correct because it follows the pattern of multiplying the previous term by 3 and adding 1.