Question

If an AP the sum of first ten terms is-150and sum of its next ten terms is -550.Find the AP.​

Answer 1

ANSWER:-

Given:

•An A.P. the sum of first 10 terms is -150 &

•Sum of its next 10 terms is -550.

To find:

The A.P.

Solution:

Let a be the first term &

Let d be the common difference.

We know that, Formula of sum of the Arithmetic Progression:

$= > nth = \frac{n}{2} (2a + (n - 1)d)$

Therefore,

${}^{s} 10 = - 150$

$= > - 150 = \frac{10}{2} (2a + (10 - 1)d) \\ \\ = > - 150 = 5(2a + 9d) \\ \\ = > \frac{ - 150}{5} = 2a + 9d \\ \\ = > - 30 = 2a + 9d \:or \\ \\ = > 2a + 9d = - 30................(1)$

&

Sum of next 10 terms= -550

Therefore,

a11, a12 , a13,........+a20= -550

=) S20 - S10 = -550

=) S20 - (-150)= -550

=) S20 +150 = -550

=) S20 = -550 - 150

=) S20= -700

So,

$= > - 700 = \frac{20}{2} (2a + (20 - 1)d) \\ \\ = > - 700 = 10(2a + 19d) \\ \\ = > \frac{ - 700}{10 } = 2a + 19d \\ \\ = > - 70 = 2a + 19d \: \: or \\ \\ = > 2a + 19d = - 70..................(2)$

Subtracting equation (1) & (2), we get;

2a + 9d = -30

2a +19d= -70

- - +

_______________

=) -10d = 40

=) d= 40/-10

=) d= -4

Putting the value of d in equation (1), we get;

=) 2a +9d = -30

=) 2a + 9(-4) = -30

=) 2a +(-36) = -30

=) 2a - 36 = -30

=) 2a = -30 +36

=) 2a = 6

=) a= 6/2

=) a= 3

Thus,

The A.P. is -1, 1,-6,-9.........

Thank You.

Answer 2

Answer:

3, -1 , -5....

Explanation: