find a5 and an for the geometric sequence: a1=8 and r= -5
The n-th term of a geometric sequence with initial value a1 and common ratio r is given by:
an = a1 ∙ r ^ ( n - 1 )
a5 = a1 ∙ r ^ ( 5 - 1 )
a5 = a1 ∙ r ^ 4
a5 = 8 ∙ ( - 5 ) ^ 4
a5 = 8 ∙ 625
a5 = 5000
To find the values of a5 and an for the given geometric sequence with a1 = 8 and r = -5, we need to find the common ratio first.
The formula for the nth term of a geometric sequence is: an = a1 * r^(n-1)
Given a1 = 8 and r = -5, we can use this formula to find a5 and an.
1. To find a5 (the 5th term), substitute n = 5 into the formula:
a5 = 8 * (-5)^(5-1)
= 8 * (-5)^4
= 8 * (625)
= 5000
Therefore, a5 = 5000.
2. To find an (the nth term), we need to know the value of n. If you provide the value of n, I can calculate the corresponding term using the formula above.
To find the terms a5 and an of a geometric sequence, we need the first term (a1) and the common ratio (r). In this case, a1 is 8 and r is -5.
The formula to find the nth term of a geometric sequence is given by:
an = a1 * r^(n-1)
Using this formula, let's find a5 and an.
a5 = a1 * r^(5-1)
= a1 * r^4
Substituting the values a1 = 8 and r = -5 into the equation, we get:
a5 = 8 * (-5)^4
Now, let's calculate this value:
a5 = 8 * 625
= 5000
So, the fifth term of the geometric sequence is a5 = 5000.
To find the general term an, we can substitute n into the formula:
an = a1 * r^(n-1)
= 8 * (-5)^(n-1)
Since an represents the nth term of the sequence, we can leave it as an expression using n.
Therefore, the formula for the nth term of the given geometric sequence is: an = 8 * (-5)^(n-1).