Consider the sequence 12, 5, -2, -9
Determine the formula for the general term of the sequence:
tn = a + (n-1)d
tn = 12 + (n-1)-7
tn = 12-7n + 7
tn = -7n + 19
I got -7n +19 as the answer, but at the back of the book, it says.. tn = 19-7n. I have no idea how the numbers got mixed up :\
Both are correct, and mathematically equivalent.
A linear expression is usually presented the way you did, i.e. the term with the variable first, followed by the constant:
-7n+19.
However, there are times that we want to get rid of the annoying leading negative sign (if there are positive terms), and place the positive term first.
To determine the formula for the general term of the sequence, we need to find the pattern or the rule that governs the sequence. Let's break down the given sequence to identify the pattern:
12, 5, -2, -9
From the given sequence, we can observe that each term is decreasing by 7.
To find the formula for the general term, we can use the formula:
tn = a + (n-1)d,
where:
tn = nth term of the sequence,
a = first term of the sequence, and
d = common difference between consecutive terms.
Applying this formula to our given sequence:
a = 12 (first term)
d = -7 (common difference)
tn = 12 + (n-1)(-7)
tn = 12 - 7n + 7
tn = -7n + 19
So, based on the pattern we observed, the correct formula for the general term of the given sequence is tn = -7n + 19. The book's answer, tn = 19 - 7n, appears to be incorrect.