The 5th and 10th terms of AP are 0,10 respectively.The 20th term is
40.
To find the common difference, we can use the formula:
nth 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 information, we know that the 5th term is 0 and the 10th term is 10. Plugging these values into the formula, we get:
5th term = a + (5-1)d = 0
10th term = a + (10-1)d = 10
Simplifying these equations, we have:
a + 4d = 0 (equation 1)
a + 9d = 10 (equation 2)
We can use these equations to find the values of a and d. Subtracting equation 1 from equation 2, we get:
9d - 4d = 10 - 0
5d = 10
d = 2
Now that we know the common difference is 2, we can find the first term of the AP using equation 1:
a + 4d = 0
a + 4(2) = 0
a + 8 = 0
a = -8
So, the first term of the AP is -8 and the common difference is 2. Using the formula for nth term, we can find the 20th term:
20th term = a + (20-1)d
20th term = -8 + (19)(2) = 40
Therefore, the 20th term of the AP is 40.
To find the 20th term of an arithmetic progression (AP), we need to determine the common difference (d) of the sequence.
Given that the 5th term is 0 and the 10th term is 10, we can find the common difference using the formula:
d = (10th term - 5th term) / (10 - 5)
= (10 - 0) / 5
= 10 / 5
= 2
Now, we can use the formula to find the nth term of an arithmetic progression:
nth term (an) = first term (a) + (n - 1) * common difference (d)
Substituting the known values:
20th term (a20) = 0 + (20 - 1) * 2
= 0 + 19 * 2
= 0 + 38
= 38
Therefore, the 20th term of the arithmetic progression is 38.
To find the 20th term of an arithmetic progression (AP), we first need to determine the common difference (d) between consecutive terms.
In this case, we are given that the 5th term is 0 and the 10th term is 10.
To find the common difference, we can use the formula:
d = (10th term - 5th term) / (10 - 5)
d = (10 - 0) / 5
d = 2
We now know that the common difference (d) is 2.
To find the 20th term, we can use the formula:
nth term = first term + (n - 1) * common difference
In this case, the first term is not given, so we will use the formula:
nth term = a + (n - 1) * d
Now we can substitute the known values into the formula:
20th term = a + (20 - 1) * 2
20th term = a + 19 * 2
20th term = a + 38
Since we do not know the first term (a), we cannot determine the exact value of the 20th term.