Determine the explicit formula for each arithmetic.
The 9th and 10th yerm of an arithmetic sequence are -24 and -30 respectively.
What is the 30th term?
d = term10 - term
=-30 -(-24) = -6
in a + 8d = -24
a - 48 = -24
a = 24
term30 = a + 29d
= 24 + 29(-6) = -150
the general formula for each term is
term(n) = a + (n-1)d
= 24 + (n-1)(-6)
= 24 - 6n + 6
= -6n + 30
To determine the explicit formula for an arithmetic sequence, we need to first find the common difference (d). The common difference is the difference between any two consecutive terms in the sequence.
In this case, we know that the 9th term is -24 and the 10th term is -30. The common difference can be found by subtracting the 9th term from the 10th term:
Common difference (d) = -30 - (-24) = -30 + 24 = -6
Now that we have the common difference (d), we can use it to find the 30th term using the explicit formula for an arithmetic sequence:
nth term = a + (n - 1)d
where a is the first term, n is the term number, and d is the common difference.
Given that the 9th term is -24 (a = -24) and the common difference is -6 (d = -6), we can substitute these values into the formula:
30th term = -24 + (30 - 1)(-6)
Simplifying further:
30th term = -24 + 29(-6)
= -24 - 174
= -198
Therefore, the 30th term of the arithmetic sequence is -198.
To find the explicit formula for an arithmetic sequence, we need to determine the common difference (d) and the first term (a₁).
Given that the 9th term (a₉) is -24 and the 10th term (a₁₀) is -30, we can calculate the common difference (d) using the formula:
d = a₁₀ - a₉
In this case, the common difference is:
d = -30 - (-24) = -6
Now that we know the common difference, we can find the first term (a₁) by substituting the values of a₉, d, and n into the formula for the nth term of an arithmetic sequence:
aₙ = a₁ + (n - 1) * d
Let's substitute the values we have: a₉ = -24, d = -6, n = 9:
-24 = a₁ + (9 - 1) * (-6)
Simplifying:
-24 = a₁ - 8 * (-6)
-24 = a₁ + 48
a₁ = -24 - 48
a₁ = -72
Now we can use the explicit formula to find the 30th term (a₃₀) by substituting the values of a₁ and n into the formula:
aₙ = a₁ + (n - 1) * d
Substituting a₁ = -72 and n = 30:
a₃₀ = -72 + (30 - 1) * (-6)
a₃₀ = -72 + 29 * (-6)
a₃₀ = -72 - 174
a₃₀ = -246
Therefore, the 30th term of the arithmetic sequence is -246.