in the sequence 100, 10, 1..., a20 is equal to what?
Okay, I know the first term is 100. But the common difference I realize you have to divide by 10 because if you subtract 100 by 90 = 10 and 10 - 9 = 1.
an = a1 + (n -1)d
This is a geometric sequence, not an arithmetic.
a = 100 and r = 1/10
does a20 stand for the 20th term?
if so, then
term(20) = ar^19
= 100(1/10)^19
= (1/10)^17
To find the value of a20 in the sequence 100, 10, 1..., we need to first determine the pattern or rule governing the sequence.
Looking at the given sequence, we can observe that each term is obtained by dividing the previous term by 10. So, the pattern that we can identify is that each term is obtained by dividing the previous term by 10.
To find a20, we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
Where:
an = the nth term
a1 = the first term
r = the common ratio
n = the position of the term we want to find
In the given sequence, we have:
a1 = 100
r = 1/10 (since we divide each term by 10)
Plugging in these values into the formula, we can find a20:
a20 = 100 * (1/10)^(20-1)
= 100 * (1/10)^19
Calculating this expression:
a20 ≈ 1.0 x 10^(-17)
Therefore, a20 in the sequence 100, 10, 1... is approximately 1.0 x 10^(-17).