Question

If the sum of the first 10 terms of a linear sequence is 15,and the sum of the next 10 terms is 215.find the sequence

Answer 1

Answer:

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Answer 2

Solution :-

Let us assume that, first term is a and common difference is d .

So,

→ S(n) = (n/2)[2a + (n - 1)d]

→ S(10) = (10/2)[2a + 9d]

→ 5(2a + 9d) = 15

→ 2a + 9d = 3 ------ Eqn.(1)

and,

→ S(10) + next 10 terms = S(20)

So,

→ S(20) = (20/2)[2a + 19d]

→ 10(2a + 19d) = 230

→ 2a + 19d = 23 ------- Eqn.(2)

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

→ (2a + 19d) - (2a + 9d) = 23 - 3

→ 10d = 20

→ d = 2

putting d in Eqn.(1),

→ 2a + 9 * 2 = 3

→ 2a = 3 - 18

→ 2a = (-15)

→ a = (-7.5)

therefore, required series is (-7.5) , (-5.5) , (-3.5) , (-1.5), _______ .

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