Math, asked by joeljoji, 7 months ago

in an ap the sum of first 10 term is -150 and the sum of it's next term is -550find the ap​

Answers

Answered by RvChaudharY50
1

Given :- in an AP the sum of first 10 term is -150 and the sum of it's next 10 term is -550 find the AP ?

Solution :-

Let us assume that, a and d be the first term and common difference of AP .

Given,

→ S10 = (-150)

→ (n/2)[2a + (n - 1)d] = (-150)

→ (10/2)[2a + (10 - 1)d] = (-150)

→ 5(2a + 9d) = (-150)

→ 2a + 9d = (-30) --------------- Eqn.(1)

also,

→ S20 - S10 = (-550) (given)

→ S20 = (-550) + S10

→ S20 = (-550) + (-150)

→ S20 = (-700)

→ (20/2)[2a + (20 - 1)d] = (-700)

→ 10(2a + 19d) = (-700)

→ 2a + 19d = (-70) ------------- Eqn.(2)

subtracting Eqn.(1) from Eqn.(2) ,

→ 2a + 19d - (2a + 9d) = (-70) - (-30)

→ 2a - 2a + 19d - 9d = (-70) + 30

→ 10d = (-40)

→ d = (-4) .

Putting d value in Eqn.(1) ,

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

→ 2a - 36 = (-30)

→ 2a = (-30) + 36

→ 2a = 6

→ a = 3 .

Therefore,

→ The AP is 3, -1, -5, -9, _________________.

Learn more :-

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