Question

In an ap sum of first ten terms is -150 and sum of the next 10 terms is -550 find ap

Answer 1

Let a and d be the frstime term and common difference of AP
ATQ
Sum of frst 10 terms = -150
n/2 (2a + (n-1) d = -150
10/2 (2a + (10-1) d = -150
5 (2a + 9d)= -150
2a + 9d = -10 ....eq (1)
Sum of nxt 10 terms = -550
Sum of 20 terms - sum of frst 10 terms = -550
Sum of 20 terms - (-150) = -550
Sum of 20 terms + 150 = -550
Sum of 20 terms = -700
10 (2a + 19d) = -700
2a + 19d = -70 ...eq (2)
By solving eq (1) & (2)
d = 8
a = -111

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.