Question

Answer the question with full calculations -

The sum of first 10 terms of an AP is (- 150) and the sum of it's next 10 terms is (- 550). Find the AP.

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Answer 1

Answer,

Let a be the first term and d the common difference.

Given: Sum of first 10 terms = S10 = (- 150)
Sum of next 10 terms = - 550
i.e. S20 - S10 = (-550)

Consider S10 = - 150
⇒ (10/2) [2a + (10 - 1)d] = - 150
⇒ 5 × [2a + 9d] = (-150)
⇒ [2a + 9d] = - 30 ………………….(1)

Now, consider S20 - S10 = - 550
⇒ (20/2) [2a + (20 - 1)d] - (10/2) [2a + (10 - 1)d] = - 550
⇒ 10 × [2a + 19d] - 5 [2a + 9d] = - 550
⇒ 10a + 145d = - 550 …………………..(2)

On subtracting equation (2) from 5 times of equation (2), we get,

- 100d = 400
⇒ d = - 4
∴ a = 1/2 (-30 - 9d)
⇒ a = 1/2 (-30 + 36)
⇒ a = 3

Therefore the AP is 3, - 1, - 5, - 9,….

Thanks!!

Answer 2

Hey there !!


Let a be the first term and d be the common difference of the given AP .


S₁₀ = -150.

⇒ Sn = n/2 [ 2a + (n-1)d]

⇒ S₁₀ = 10/2 [ 2a + ( 10 - 1 ) d ].

⇒ -150= 10/2 [ 2a + 9d ]

⇒ -150 = 5 [ 2a + 9d ]

⇒ -30 = 2a + 9d

⇒2a + 9d = -30...........(1)


Clearly, the sum 20 term = - 150 + (-550) .

⇒ S₂₀ = -700

⇒ Sn = n/2 [ 2a + (n-1)d]

⇒ S₂₀ = 20/2 [ 2a + ( 20 - 1 )d ] .

⇒ -700   = 20/2 [ 2a + 19d ]

⇒ -700  = 10 [ 2a + 19d ]

⇒ -70 = 2a + 19d .

⇒ 2a + 19d = -70........(2)

Substracting 1 and 2 , we get 
  
2a + 19d = -70
2a + 9d = -30
-     -     +
____________
⇒ 10d = -40

⇒ d = -40/10 = -4


Put the value of d in equation 1.

2a + 9d = -30

⇒ 2a -36 = -30

⇒ 2a = -30+36

⇒ a = 6/2 = 3

a = 3

d = -4

Hence, AP is 3,-1,-5, - 9 ....


THANKS


#BeBrainly.