The 5th and 10th term of an AP are 0 and 10 in respectively.find the 20th term.
A20=a10 + 10d=
5th and 10th term of an AP are 0 and 10
a+4d = 0
a+9d = 10
subtract
5d = 10
d = 2
a + 4(2) = 0
a + 8 = 0
a = -8
term(20) = a + 19d = .....
the 10th term is 5 differences beyond the fifth
5 d = 10 - 0 ... d = 2
To find the 20th term of an arithmetic progression (AP), we need to identify the common difference (d) in the sequence.
Given that the 5th term (a5) is 0 and the 10th term (a10) is 10, we can construct the following equations:
a5 = a1 + (5-1)d ...(1)
a10 = a1 + (10-1)d ...(2)
From equation (1), we have:
0 = a1 + 4d ...(3)
From equation (2), we have:
10 = a1 + 9d ...(4)
Now, we can solve equations (3) and (4) simultaneously to find the values of a1 and d.
Subtracting equation (3) from equation (4) gives us:
10 - 0 = (a1 + 9d) - (a1 + 4d)
10 = 5d
d = 10/5
d = 2
Now that we know the value of d, we can substitute it into equation (3) to determine the value of a1:
0 = a1 + 4(2)
0 = a1 + 8
a1 = -8
Now we have the first term (a1 = -8) and the common difference (d = 2) of the AP.
To find the 20th term (a20), we can use the formula for the nth term of an arithmetic progression:
an = a1 + (n-1)d
Substituting the values we found:
a20 = -8 + (20-1)(2)
a20 = -8 + 19(2)
a20 = -8 + 38
a20 = 30
Therefore, the 20th term of the arithmetic progression is 30.