Question

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Find the sum of 11 terms of an AP whose middle term is 20??????.

Answer 1

As 11 is a Odd Number - We can Notice that in a series of 11 terms : the Middle term will the 6th Term (Because First Five terms + 6th Number + Last Five terms = Total Eleven Terms)

⇒ Given that 6th Term is 20

We know that nth term of an AP is given by : a + (n - 1)d

⇒ 6th term (a₆) = a + (6 - 1)d = a + 5d

⇒ a + 5d = 20

Sum of 'n' terms is given by : Sn = n/2 × { a + a + (n - 1)d }

⇒ Sum of 11 terms = S₁₁ = 11/2 × { 2a + (11 - 1)d }

⇒ S₁₁ = 11/2 × { 2a + 10d }

⇒ S₁₁ = 11/2 × { 2(a + 5d) }

But we found that a + 5d = 20

⇒ S₁₁ = 11/2 × { 2 × 20 }

⇒ S₁₁ = 11/2 × 40

⇒ S₁₁ = 11 × 20 = 220

So, the Sum of 11 terms of the Given AP is 220