write an explicit formula for the sequence 7,2,-3,-8,-13 then find a14
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To find the explicit formula for the given sequence, we can observe that each successive term is obtained by subtracting 5 from the previous term. Therefore, the explicit formula for this sequence is:
an = 7 - 5n
Where n represents the position of the term in the sequence.
To find a14, substitute n = 14 into the formula:
a14 = 7 - 5(14)
= 7 - 70
= -63
Therefore, a14 is -63.
To write an explicit formula for the given sequence, we need to identify the pattern or relationship between the terms. From the given sequence (7, 2, -3, -8, -13), we can observe that each term is obtained by subtracting 5 from the previous term. Therefore, the explicit formula for this sequence can be written as:
a_n = a_1 + (n - 1) * d
where:
a_n = the nth term of the sequence
a_1 = the first term of the sequence
n = the position of the term in the sequence
d = the common difference between terms
In this case, a_1 = 7 (the first term) and d = -5 (the common difference).
Now, let's find the value of a_14 using the explicit formula:
a_14 = a_1 + (14 - 1) * d
= 7 + 13 * (-5)
= 7 - 65
= -58
Therefore, the value of a_14 is -58.
There won't be any 14 in that sequence, unless you want the 14th number.
If X is the value of the n'th number in the sequence (starting with n=1)
X = 12 - 5n