Bunuel wrote:
The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the thirty-fifth term in the sequence?
A. 2
B. 4
C. 7
D. 9
E. 13
Kudos for a correct solution.
800score Official Solution:(To understand units and tens, in 75 7 is tens and 5 is units.) We cannot reasonably be expected to write the sequence to the thirty-fifth term. We should therefore expect a repeating pattern within the tens and units digits of the sequence.
Let’s write out the first 8 terms and see what the pattern is:
2, 7, 22, 67, 202, 607, 1822, 5467.
Examining the tens and units digits, we see that the following four-term pattern repeats in those digits:
02, 07, 22, 67, etc.
To find what the tens and units digits of the thirty-fifth term will be, we must first divide the term number (35) by the number of terms in the repeating sequence (4):
35/4 = 8 remainder 3.
This means the four-term sequence fully repeats 8 times, and the remainder tells us how many terms into the repeating sequence the term in question will be.
Three terms into the repeating sequence, the tens and units digits are both 2. The sum of these digits is the answer to the question:
2 + 2 = 4.
The correct answer is choice (B). _________________