Question
The 5th and 10th terms of AP are 0,10 respectively.The 20th term is
Answers
GPT 3.5
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 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.