Question

34+32+30+... +10 find the sum of A.P
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Answer 1

Step-by-step explanation:

This is the perfect answer.

Answer 2

EXPLANATION.

Sum of arithmetic progression.

⇒ 34 + 32 + 30 + . . . . . + 10.

As we know that,

General term of an ap.

⇒ Aₙ = a + (n - 1)d.

Using this formula in the equation, we get.

First term = a = 34.

Common difference = d = b - a = 32 - 34 = - 2.

⇒ aₙ = 10.

Put the values in the equation, we get.

⇒ 10 = 34 + (n - 1)(-2).

⇒ 10 = 34 + (- 2n + 2).

⇒ 10 = 34 - 2n + 2.

⇒ 10 = 36 - 2n.

⇒ 10 - 36 = - 2n.

⇒ - 26 = - 2n.

⇒ n = 13.

As we know that,

Sum of nth term of an ap.

⇒ Sₙ = n/2[2a + (n - 1)d].

Put the values in the equation, we get.

⇒ Sₙ = 13/2[2 x 34 + (13 - 1)(-2)].

⇒ Sₙ = 13/2[68 + (12)(-2)].

⇒ Sₙ = 13/2[68 - 24].

⇒ Sₙ = 13/2[44].

⇒ Sₙ = 13 x 22.

⇒ Sₙ = 286.

Sum of an ap = 286.