Question

in an ap the sum of first ten terms is -150 and the sum of its next ten terms is -550.find the ap

Answer 1

S10 = -150
S20 = S10 + S10
       =  -550 + -150
       = -700
 S10 =-150
         = 2a + 9d = -150/5 = -30 ----------------------eq no 1
 S20 =-700
         =2a + 19d = -700/10 = -70 --------------------eq no 2
   solving 1 and 2 we get,
                                       a = 3  and d = -4
           and the ap is        3, -1, -5, etc

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.