The sum of 8th term of an A.P is 60 while the sum of 50th term is 880. Find the 43rd term

sum(8) = (8/2)(2a + 7d) = 60

2a + 7d = 15

sum(50) = (50/2)(2a + 49d) = 880
2a + 49d = 35.2
subtract them:
42d = 20.2
d = 202/420 = 101/210
2a + 7(101/210) = 15
2a = 349/30
a = 349/60

term(43) = a + 42d
= 349/60 + 42(101/210
= 1561/60

8/2 (2a+7d) = 50

50/2 (2a+49d) = 880

Solve for a and d, and then evaluate

a+42d

To find the 43rd term of an arithmetic progression (A.P), we need to know the first term (a) and the common difference (d).

Since we are given the sum of the 8th term and the sum of the 50th term, we can use the formula for the sum of an A.P. to find these values:

Sum of the 8th term:
Sn = (n/2)(2a + (n-1)d) [Formula for the sum of an A.P]
60 = (8/2)(2a + (8-1)d)
60 = 4(2a + 7d)
15 = 2a + 7d [Equation 1]

Sum of the 50th term:
Sn = (n/2)(2a + (n-1)d)
880 = (50/2)(2a + (50-1)d)
880 = 25(2a + 49d)
35 = 2a + 49d [Equation 2]

Now, we have two equations with two variables (a and d). We can solve this system of equations to find the values of a and d.

Multiplying Equation 1 by 2 and subtracting Equation 2:
(2a + 7d) - (2a + 49d) = 15 - 35
-42d = -20
d = -20/-42
d = 10/21

Now substitute the value of d into Equation 1 to find a:
15 = 2a + 7(10/21)
15 = 2a + 70/21
15 - 70/21 = 2a
(315 - 70)/21 = 2a
245/21 = 2a
a = 245/42
a = 5.83 (rounded to two decimal places)

Now that we have found the values of a and d, we can find the 43rd term:
43rd term = a + (n-1)d
43rd term = 5.83 + (43-1)(10/21)
43rd term = 5.83 + 42(10/21)
43rd term = 5.83 + 20
43rd term = 25.83

Therefore, the 43rd term of the A.P is approximately 25.83.