hi
if the second term of a sequence is root(2) and the seventh term is 8 what is the nth term equation(Geometric sequence)
thanks
ar = √2
ar^6 = 8
ar^6/ar = r^5 = 8/√2 = (√2)^6/√2 = √2^5
so, r= √2, a=1
Tn = ar^(n-1) = √2^(n-1)
Hi! In a geometric sequence, each term is found by multiplying the previous term by a constant number called the common ratio (denoted by 'r').
To find the common ratio in this case, we can divide the seventh term by the second term:
r = 8 / √2
Now that we know the common ratio, we can write the nth term equation for a geometric sequence. The general form of the nth term equation for a geometric sequence is:
an = a1 * r^(n-1)
In this equation:
- 'an' represents the nth term of the sequence.
- 'a1' represents the first term of the sequence.
In your case, the second term is given as √2, so the first term 'a1' would be the second term divided by the common ratio:
a1 = √2 / r
Now we can rewrite the nth term equation for the geometric sequence:
an = (√2 / r) * r^(n-1)
Simplifying this equation further, we have:
an = √2 * r^(n-2)
Therefore, the nth term equation for the given geometric sequence is:
an = √2 * (8 / √2)^(n-2)
This equation will give you the value of the nth term in the sequence.