1.) In the following problem, write the first five of the terms of the arithmetic sequence.
a1=16.5
d=0.25
2.) Find a the correct formula for the an for the arithmetic sequence.
a1=-1
d=5
(1)
In arithmetic sequence, we just add the common difference, d = 0.25, to a term to get the next term. Therefore,
a1 = 16.5
a2 = 16.5 + 0.25 = 16.75
a3 = 16.75 + 0.25 = 17.0
...and so on.
(2)
General formula for arithmetic sequence:
an = ao + (n-1)d
where
an = nth term
ao = first term
n = number of terms
d = common difference
Since you have a1 = -1 and d = 5, thus,
an = -1 + 5(n-1)
hope this helps~ `u`
1.)
a1 = 16.5
a2 = 16.5 + 0.25 = 16.75
a3 = 16.75 + 0.25 = 17
a4 = 17 +0.25 = 17.25
a5 = 17.25 +0.25 = 17.5
2.)
an = a1 + ( n - 1 ) * d
an = - 1 + ( n - 1 ) * 5
OR
an = 5 ( n - 1 ) - 1
To find the first five terms of an arithmetic sequence, we'll use the formula for the nth term (an) of an arithmetic sequence:
(a_n) = a_1 + (n-1)d
where a_n is the nth term, a_1 is the first term, n is the position of the term, and d is the common difference.
1.) In this case, we have:
a_1 = 16.5
d = 0.25
To find the first five terms, we substitute the values of a_1 and d into the formula:
(a_1) = 16.5 + (1-1) * 0.25 = 16.5 + 0 = 16.5 (the first term is 16.5)
(a_2) = 16.5 + (2-1) * 0.25 = 16.5 + 0.25 = 16.75
(a_3) = 16.5 + (3-1) * 0.25 = 16.5 + 0.5 = 17
(a_4) = 16.5 + (4-1) * 0.25 = 16.5 + 0.75 = 17.25
(a_5) = 16.5 + (5-1) * 0.25 = 16.5 + 1 = 17.5
Therefore, the first five terms of the arithmetic sequence are: 16.5, 16.75, 17, 17.25, 17.5.
2.) To find a generic formula for the nth term of an arithmetic sequence, we'll use the same formula:
(a_n) = a_1 + (n-1)d
In this case:
a_1 = -1
d = 5
Substituting the values into the formula, we get:
(a_n) = -1 + (n-1) * 5
Simplifying further:
(a_n) = -1 + 5n - 5 = 5n - 6
Therefore, the correct formula for the nth term (a_n) in this arithmetic sequence is 5n - 6.
1.) To find the first five terms of an arithmetic sequence, we can use the formula:
an = a1 + (n - 1)d
where:
an = nth term of the sequence
a1 = first term of the sequence
d = common difference between terms
n = number of terms in the sequence
In this case, we are given:
a1 = 16.5
d = 0.25
Let's substitute these values into the formula for n = 1 to 5:
For n = 1:
a1 = 16.5 + (1 - 1)(0.25) = 16.5
For n = 2:
a2 = 16.5 + (2 - 1)(0.25) = 16.75
For n = 3:
a3 = 16.5 + (3 - 1)(0.25) = 17
For n = 4:
a4 = 16.5 + (4 - 1)(0.25) = 17.25
For n = 5:
a5 = 16.5 + (5 - 1)(0.25) = 17.5
Therefore, the first five terms of the arithmetic sequence are:
16.5, 16.75, 17, 17.25, and 17.5.
2.) To find the formula for an in an arithmetic sequence, we can use the same formula as before:
an = a1 + (n - 1)d
In this case, we are given:
a1 = -1
d = 5
Substituting these values into the formula, we have:
an = -1 + (n - 1)(5)
Expanding the equation, we get:
an = -1 + 5n - 5
Combining like terms, we have:
an = 5n - 6
Therefore, the correct formula for an in the given arithmetic sequence is:
an = 5n - 6.