To find the sixth term of the AP, we need to find the pattern of the AP.
The given pattern is k, 2k/3, k/3, 0... r.
From this pattern, we can see that the common difference between each term is -k/3.
Therefore, to find the sixth term, we can add (-k/3) to the third term:
6th term = k/3 + (-k/3)
= 0
So, the sixth term is 0.
To find the value of k when the 20th term is equal to 15, we can use the formula for the nth term of an AP:
n-th term = a + (n-1)d
where a is the first term, d is the common difference, and n is the term number.
From the given pattern, we know that the first term is k and the common difference is -k/3.
Using the formula, we can substitute the values:
20th term = k + (20-1)(-k/3)
= k - (19/3)k
= (1 - 19/3)k
= (3/3 - 19/3)k
= (-16/3)k
Given that the 20th term is equal to 15, we can set up the equation:
(-16/3)k = 15
To solve for k, we can multiply both sides of the equation by -3/16:
k = 15 * (-3/16)
= -45/16
Therefore, k is equal to -45/16.
An A . P is given by k, 2k/3,k/3,0... r
(I)find the sixth term
(Ii)if the 20 term is equal to 15,find k.
3 answers
The first term of geometric series is 4.what is the sum of the first 6 term
of the series if the common ratio is 3 .
of the series if the common ratio is 3 .
To find the sum of the first 6 terms of a geometric series, we can use the formula:
S_n = a * (r^n - 1) / (r - 1)
Where S_n is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
In this case, the first term (a) is 4 and the common ratio (r) is 3. We want to find the sum of the first 6 terms (n = 6).
Plugging these values into the formula, we get:
S_6 = 4 * (3^6 - 1) / (3 - 1)
Simplifying this equation, we have:
S_6 = 4 * (729 - 1) / 2
= 4 * 728 / 2
= 1456
So, the sum of the first 6 terms of the geometric series is 1456.
S_n = a * (r^n - 1) / (r - 1)
Where S_n is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
In this case, the first term (a) is 4 and the common ratio (r) is 3. We want to find the sum of the first 6 terms (n = 6).
Plugging these values into the formula, we get:
S_6 = 4 * (3^6 - 1) / (3 - 1)
Simplifying this equation, we have:
S_6 = 4 * (729 - 1) / 2
= 4 * 728 / 2
= 1456
So, the sum of the first 6 terms of the geometric series is 1456.