find the 15th term in the geometric sequenc below 20,10,5,2.5,....
a. - 25 b. - 5
4096 4096
c. 5 d. 25
4096 4096
-25
To find the 15th term in the given geometric sequence, we need to determine the common ratio and use it to find the 15th term.
To find the common ratio, we divide any term by the previous term. Let's divide the second term, 10, by the first term, 20:
10/20 = 0.5
So, the common ratio is 0.5.
To find the 15th term, we can use the formula for the nth term of a geometric sequence:
tn = a * r^(n-1)
where:
tn = the nth term
a = the first term
r = the common ratio
n = the term number
Plugging in the values:
a = 20 (the first term)
r = 0.5 (the common ratio)
n = 15 (the term number we want to find)
t15 = 20 * 0.5^(15-1)
Simplifying the equation:
t15 = 20 * 0.5^14
Calculating:
t15 ≈ 20 * 0.00006103515625
t15 ≈ 0.001220703125
So, the 15th term in the given geometric sequence is approximately 0.001220703125.
Therefore, none of the given options (a, b, c, d) matches the solution.
To find the 15th term in the geometric sequence, we need to find the common ratio first. The common ratio is found by dividing any term in the sequence by its preceding term.
Let's divide the second term (10) by the first term (20):
10/20 = 0.5
We can see that the common ratio is 0.5.
To find the 15th term, we can use the formula for finding the nth term of a geometric sequence:
nth term = first term * common ratio^(n-1)
Plugging in the values:
15th term = 20 * 0.5^(15-1)
Calculating 0.5^(15-1):
0.5^14 = 0.00006103515625
Multiplying this by the first term:
15th term = 20 * 0.00006103515625 ≈ 0.001220703125
Looking at the options given, we can see that none of them match this result.