Write an explicit formula for the sequence. Use this, to find the 80th term of the sequence that begins: -3,1,5,9....
Why is it minus seven instead of any other number?
To find an explicit formula for the sequence, we need to observe the pattern and figure out the relationship between each term and its position.
Looking at the given sequence, we can see that each term is increasing by 4. In other words, the difference between each pair of consecutive terms is constant.
Let's denote the first term of the sequence as a₁ and the common difference between the terms as d. In this case, a₁ = -3 and d = 4.
The explicit formula for an arithmetic sequence is given by the equation:
an = a₁ + (n - 1)d
Substituting the given values, we have:
an = -3 + (n - 1)4
Now, we can find the 80th term by substituting n = 80 into the formula:
a80 = -3 + (80 - 1)4
Simplifying the equation:
a80 = -3 + 79 * 4
Calculating further:
a80 = -3 + 316
Finally, we find:
a80 = 313
Therefore, the 80th term of the sequence is 313.
each number is four greater than the preceding number
... the common difference , d, equals four
An = 4 n - 7