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