find the 4th term of an arithmetic sequence whose first term is -8 and whose 9th term is 32.
32-(-8) = 40 = 8d, so d = 5
-8+3*5 = 7
or,
T4 = T1 + 3*(T9-T1)/8
the ninth term is -8+(9-1)d and that is equal to 32. solve for d, then find the 4 term
A(4)=-8+d(4-1)
To find the 4th term of an arithmetic sequence, we first need to determine the common difference.
The common difference (d) can be calculated using the formula:
d = (nᵗʰ term - first term) / (n - 1)
Using the given information:
First term (a₁) = -8
9th term (a₉) = 32
We can substitute these values into the formula:
d = (a₉ - a₁) / (9 - 1)
d = (32 - (-8)) / 8
d = 40 / 8
d = 5
Now that we know the common difference is 5, we can find the 4th term (a₄) using the formula:
a₄ = a₁ + (n - 1) * d
Substituting the known values:
a₁ = -8
n = 4
d = 5
a₄ = -8 + (4 - 1) * 5
a₄ = -8 + 3 * 5
a₄ = -8 + 15
a₄ = 7
Therefore, the 4th term of the arithmetic sequence is 7.
To find the 4th term of an arithmetic sequence, we need to use the formula:
\(a_n = a_1 + (n-1)d\)
where:
\(a_n\) is the value of the nth term,
\(a_1\) is the value of the first term,
\(n\) is the term number, and
\(d\) is the common difference.
Given that the first term (\(a_1\)) is -8, we can substitute this value into the formula:
\(a_n = -8 + (n-1)d\)
We are also given that the 9th term (\(a_9\)) is 32. Let's substitute this information into the formula to find the common difference (\(d\)):
\(a_9 = -8 + (9-1)d\)
\(32 = -8 + 8d\)
\(40 = 8d\)
\(d = 40/8\)
\(d = 5\)
Now that we know the common difference (\(d\)), we can substitute it back into the formula to find the 4th term (\(a_4\)):
\(a_4 = -8 + (4-1)5\)
\(a_4 = -8 + 3 \times 5\)
\(a_4 = -8 + 15\)
\(a_4 = 7\)
Therefore, the 4th term of the arithmetic sequence is 7.