In an A.P., the sum of first ten terms is −150 and the sum of its next ten terms is −550. Find the A.P.
Answers
Answer:
The AP is 3, - 1,- 5 ,- 9,…...
Step-by-step explanation:
Given :
S10 = - 150 and sum of its next 10 terms is - 550.
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
S10 = (10/2) [ 2a + (10 - 1)d ]
-150 = 10/2 [2a + 9d]
-150 = 5[2a + 9d]
-150/5 = 2a + 9d
- 30 = 2a + 9d
2a + 9d = - 30 ………...(1)
And
Sum of its next 10 terms = - 550 (Given)
Sum of first 20 terms = Sum of first 10 terms + Sum of next 10 terms.
S20 = - 150 + (-550)
S20 = - 150 - 550
S20 = - 700
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
S20 = (20/2) [ 2a + (20 - 1)d ]
-700 = 10 [ 2a + 19d ]
-700/10 = 2a + 19d
2a + 19d = -70 ………... (2)
On subtracting eq (1) from (2)
2a + 19d = -70
2a + 9d = - 30
(-) (-) (+)
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10d = - 40
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d = - 40/10
d = - 4
On putting the value of d = - 4 in eq (1),
2a + 9d = - 30
2a + 9(- 4) = - 30
2a - 36 = - 30
2a = - 30 + 36
2a = 6
a = 6/2
a = 3
First term,a = 3
The required AP is a, a + d , a + 2d , a + 3d , a + 4d ……
Hence, the AP is 3, - 1,- 5 ,- 9,…...
HOPE THIS ANSWER WILL HELP YOU…..
Answer:
3,-1, -5, -9....
Step-by-step explanation:
Please refer to the picture...
Hope it helps...
