1, 7, 49, 343, …
- Each term in the sequence above after the first one is determined by multiplying the previous term by 7. What will be the units (ones) digit of the 96th term?
(A) 9
(B) 7
(C) 5
(D) 3
(E) 1
Answer and explanation below:
Usually, when the SAT asks you to find something like the 96th term, they’re really asking you to recognize the pattern that exists in all the terms. Fill the sequence in a little more and the pattern should reveal itself:
1, 7, 49, 343, 2401, 16807, 117649,…
See it? The units digits follow a very simple pattern: 1, 7, 9, 3, 1, 7, 9, 3, etc.
So now all you need to do is figure out the 96th term. Every 4th term is 3, and 96 is evenly divisible by 4, so the 96th term has to be 3!
(D) is your answer.
Comments (3)
Hi Mike. Really learning a lot from your book. I have a question regarding a similar question in your book about patterns. It is #18 on page 87. I am confused as to why you decide that the 1 billionth term is a multiple of the 4th term- it is also a multiple of 2nd term and 1st term. Why do you always seek the greatest divisor? You mention to keep things easy to start at the end of the set, but why? Also, when you divide 1 billion by 4, you get a whole number. What does this number tell you? Thank you so much!
Not that 1 billion is a multiple of the 4th TERM, just that it’s a multiple of 4. What matters is that the pattern repeats every 4 terms, so we want to know where 1 billion falls relative to multiples of 4. I just replied to your comment on the Q&A in more detail—hopefully that helps!
Even here, the third term is a factor of 96– why wouldn’t you say that the unit of the 96th term would be 9?