Bunuel wrote:
The \(n_{th}\) term (\(t_n\)) of a certain sequence is defined as \(t_{n}\) = \(t_{n-1}\) \(+4\). If \(t_{1}\) =−7 then \(t_{71} =\)
A. 273
B. 277
C. 281
D. 283
E. 287
Kudos for correct solution.
If we don't already know the formula for arithmetic sequences, we can still answer the question.
The given formula tells us that each term in the sequence is
4 greater than the term before it.
So, let's list some terms to see if we can
see a patternterm1 =
-7term2 =
-7 + 4term3 =
-7 + 4 + 4term4 =
-7 + 4 + 4 + 4term5 =
-7 + 4 + 4 + 4 + 4.
.
.
At this point we can probably see the patternSo, term71 =
-7 + 4 + 4 + 4 + 4 + 4 + 4 + 4.......
QUESTION: How many 4's are in the sum for term71?Well, term1 has 0
4's
term2 has 1
4term3 has 2
4's
term4 has 3
4's
etc
So, we can see that term71 has 70
4's
In other words, term71 =
-7 + (70)(
4)
=
-7 + 280
= 273
Answer: A
Cheers,
Brent