The 9th term of AP is 52 while the 12th term is 70 find the it's 20 terms
Let's assume the first term (a) of the arithmetic progression (AP) is 'x' and the common difference (d) is 'y'.
We know that the 9th term of the AP is 52, so we can write the equation:
a + (9-1)y = 52
Simplifying and rearranging the equation, we get:
x + 8y = 52 ..........(Equation 1)
We also know that the 12th term of the AP is 70, so we can write the equation:
a + (12-1)y = 70
Simplifying and rearranging the equation, we get:
x + 11y = 70 ..........(Equation 2)
Now, let's solve these two equations to find the values of x and y.
Multiplying Equation 1 by 11 and Equation 2 by 8, we get:
11x + 88y = 572 ..........(Equation 3)
8x + 88y = 560 ..........(Equation 4)
Subtracting Equation 4 from Equation 3, we get:
11x - 8x = 572 - 560
3x = 12
x = 4
Substituting the value of x in Equation 1, we get:
4 + 8y = 52
8y = 48
y = 6
So, we have found that the first term (a) of the AP is 4 and the common difference (d) is 6.
Now, let's find the 20th term of the AP:
The 20th term can be represented as:
a + (20-1)y
Substituting the values of a and y, we get:
4 + (20-1)(6)
4 + 19(6)
4 + 114
= 118
Therefore, the 20th term of the AP is 118.