Question

solve the sum of the first 9 terms of an A.P is 72 and the sum of the next 4 terms is72 .find the A.P.

Answer 1

answer

Answer 2

stop posting the same question over and over.

sometimes it takes a while for someone to stop by who feels able to help.
See your first posting of this. Apparently you haven't been working on it in the meantime.

Answer 3

noone will help ya if you keep re-posting kid.

Answer 4

[AI-generated answer — Explain Bot]

To solve this problem, we will use the formulas for the sum of arithmetic progression (A.P).

The sum of the first n terms of an A.P is given by the formula:
Sn = (n/2)(2a + (n-1)d)

where Sn is the sum of the first n terms, a is the first term, and d is the common difference of the A.P.

Given that the sum of the first 9 terms is 72, we can write the equation:
S9 = (9/2)(2a + (9-1)d) = 72

Simplifying this equation, we get:
9(2a + 8d) = 144
2a + 8d = 16 ------------(Equation 1)

We are also given that the sum of the next 4 terms is 72. So the sum of the next 4 terms starting from the 10th term is 72.
S4 = (4/2)(2(a + 9d) + (4-1)d) = 72

Simplifying this equation, we get:
4(2a + 26d) = 144

2a + 26d = 36 ------------(Equation 2)

Now, we have two equations with two variables (a and d). We can solve these equations simultaneously to find the values of a and d, which will give us the A.P.

Subtracting Equation 1 from Equation 2, we have:
(2a + 26d) - (2a + 8d) = 36 - 16
18d = 20

Dividing both sides by 18, we get:
d = 20/18
d = 10/9

Substituting the value of d in Equation 1, we have:
2a + 8(10/9) = 16
2a + 80/9 = 16
2a = 16 - 80/9
2a = 144/9 - 80/9
2a = 64/9

Dividing both sides by 2, we get:
a = (64/9) / 2
a = 64/18
a = 32/9

Therefore, the first term (a) of the A.P is 32/9 and the common difference (d) is 10/9.

So, the A.P is: 32/9, 70/9, 108/9, 146/9, 184/9, 222/9, 260/9, 298/9, 336/9, ...