the 9th term of an AP is 52 while the 12th term is 70.find the sum of its 20th term

a+8d=52

a+11d=70
subtract ....
3d = 18
d=6

sub into the 1st equation to find a, then
sum(20) = (2//2)[2a + 19d ]

the answer is 247

The 9th term

To find the sum of the 20th term of an arithmetic progression (AP), we need to find the first term (a) and the common difference (d).

Given that the 9th term (a9) is 52 and the 12th term (a12) is 70, we can use this information to find the common difference (d).

First, we find the ninth term using the formula: a9 = a + 8d. Substituting the values we have: 52 = a + 8d.

Similarly, we find the twelfth term using the formula: a12 = a + 11d. Substituting the values we have: 70 = a + 11d.

Now we have two equations:
Equation 1: 52 = a + 8d
Equation 2: 70 = a + 11d

Subtracting Equation 1 from Equation 2, we eliminate 'a':
70 - 52 = (a + 11d) - (a + 8d)
18 = 3d

Now we can find the value of 'd':
d = 18/3
d = 6

Using the value of 'd', we can substitute it back into Equation 1 to find the first term, 'a':
52 = a + 8(6)
52 = a + 48
a = 52 - 48
a = 4

Now we have the first term 'a' (4) and the common difference 'd' (6). We can use the formula for the sum of an AP to find the sum of the 20th term:

Sn = (n/2)(2a + (n-1)d)

Substituting the values we have:
S20 = (20/2)(2(4) + (20-1)(6))
S20 = 10(8 + 19)(6)
S20 = 10(27)(6)
S20 = 1620

Therefore, the sum of the 20th term of the arithmetic progression is 1620.