The 5th and 10th term of an AP are 0 and 10 respectively.find the 20th term.
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Sorry. I was at school at that time lol
5d = 5, so d = 2
a20 = a10 + 10d = ____
To find the 20th term of an arithmetic progression (AP) given the 5th and 10th terms, we need to find the common difference (d) between the terms first.
In an AP, the nth term (Tn) is given by the formula:
Tn = a + (n-1)d,
where Tn is the nth term, a is the first term, n is the position of the term, and d is the common difference.
We are given that the 5th term (T5) is 0, so we can substitute these values into the formula:
0 = a + (5-1)d.
Similarly, we are given that the 10th term (T10) is 10, so we can substitute these values into the formula:
10 = a + (10-1)d.
Now we have two equations with two unknowns (a and d):
Equation 1: 0 = a + 4d
Equation 2: 10 = a + 9d
We can solve these equations to find the values of a and d:
Equation 1 can be rewritten as a = -4d.
Substituting this into Equation 2: 10 = (-4d) + 9d.
Simplifying the equation: 10 = 5d.
Now we can solve for d: d = 10/5 = 2.
We have found the common difference, d = 2.
To find the 20th term (T20), we can use the formula: Tn = a + (n-1)d.
Substituting the values we know:
T20 = a + (20-1)2
= a + 19(2)
Since we still don't know the first term (a), we can substitute the value of d back into Equation 1 to find a:
0 = a + 4(2)
0 = a + 8
Solving for a: a = -8.
Now we have the first term (a = -8) and the common difference (d = 2), we can calculate the 20th term:
T20 = -8 + 19(2)
= -8 + 38
= 30.
Therefore, the 20th term of the arithmetic progression is 30.