A following give a geometric sequence 2,p,q,250,find the 11th term when p=10 and q=50
The difference between them is 5, so multiply 250 by 5, then multiply 1250 by 5, and so until you reach the 11th term.
Let me know if this helps!😀
If p = 10 and q = 50 the terms are:
2 , 10 , 50 , 25
The n-th term of a geometric sequence:
xn = a rⁿ⁻¹
where a is the the first term and r is the common ratio.
in this case a = 2 , r = 5
x11 = a r¹¹⁻¹ = a r¹⁰ = 2 ∙ 5¹⁰ = 2 ∙ 9 765 625 = 19 531 250
To find the 11th term of the geometric sequence, we need to determine the common ratio (r) first.
In a geometric sequence, each term is found by multiplying the preceding term by the common ratio. So, to find r, we can divide any term by its preceding term.
In this case, we can divide 'q' by 'p' since 'q' is the term following 'p'. So, r = q/p.
Substituting the given values p = 10 and q = 50, we can find the common ratio:
r = q/p = 50/10 = 5.
Now that we know the common ratio (r = 5), we can find the 11th term using the formula for geometric sequences:
an = a1 * r^(n-1),
where 'an' represents the nth term, 'a1' is the first term, 'r' is the common ratio, and 'n' is the term number we want to find.
Given that the first term 'a1' is 2, and we want to find the 11th term, we can substitute these values into the formula:
a11 = 2 * 5^(11-1).
Now we can calculate the 11th term:
a11 = 2 * 5^10.