The 4th term of an exponential sequence is 108 and the common ratio is 3. Calculate the value of the eighth term of the sequence.
We can use the formula for the nth term of an exponential sequence:
a_n = a_1 * r^(n-1)
where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.
We are given that the 4th term is 108 and the common ratio is 3. So we can use these values to find the first term:
a_4 = a_1 * 3^(4-1)
108 = a_1 * 3^3
a_1 = 4
Now we can use this value of a_1 and the common ratio to find the eighth term:
a_8 = a_1 * 3^(8-1)
a_8 = 4 * 3^7
a_8 = 4 * 2187
a_8 = 8748
Therefore, the value of the eighth term of the sequence is 8748.
Term n = a r^(n-1)
they tell us r = 3
Term n = a * 3^(n-1)
Term 4 = a * 3^3 = 27 a = 108
so
a = 4
so in general
Tn = 4 * 3 ^(n-1)
T8 = 4 * 3^7 = 4 * 2187 = 8748
Wow -- I agree with the bot !!!!
To find the value of the eighth term in an exponential sequence with a common ratio, we can use the formula:
\(T_n = ar^{(n-1)}\)
where \(T_n\) is the nth term, \(a\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.
In this case, we are given that the 4th term is 108 and the common ratio is 3. Let's plug these values into the formula:
\(108 = a \cdot 3^{(4-1)}\)
Simplifying,
\(108 = a \cdot 3^3\)
To find the value of 'a', we need more information or another equation. Without this information, we cannot calculate the value of the eighth term.
To find the value of the eighth term in the exponential sequence, you need to first determine the first term of the sequence. Once you have the first term, you can use the common ratio to calculate subsequent terms until you reach the eighth term.
To find the first term, you can use the formula for the nth term of an exponential sequence:
\[a_n = a_1 \times r^{(n-1)}\]
where \(a_n\) is the nth term, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the position of the term in the sequence.
Given that the fourth term, \(a_4\), is 108, we can substitute these values into the formula:
\[108 = a_1 \times 3^{(4-1)}\]
Simplifying this equation, we get:
\[108 = a_1 \times 3^3\]
\[108 = a_1 \times 27\]
Now we can solve for \(a_1\) by dividing both sides of the equation by 27:
\[a_1 = \frac{108}{27}\]
\[a_1 = 4\]
So, the first term, \(a_1\), of the exponential sequence is 4.
Now we can use the formula to calculate the eighth term, \(a_8\). Plugging in the values into the formula, we get:
\[a_8 = a_1 \times 3^{(8-1)}\]
\[a_8 = 4 \times 3^7\]
\[a_8 = 4 \times 2187\]
\[a_8 = 8748\]
Therefore, the value of the eighth term in the exponential sequence is 8748.