Question

3rd term of AP is 9 and its 9 term is 21 find the sum of its 40 terms.​

Answer 1

Answer:

1460

Step-by-step explanation:

Formula for nth term of AP is

tₙ = a + (n-1)d

t₃ = a + 2d = 9      -------> [1]

t₉ = a + 8d = 21    --------> [2]

Solve [1] and [2],

a + 8d  = 21

a + 2d  =  9

-  -           -

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6d = 12 => d = 2.

Substitute value of d in [1]

a +2d = 9 => a + 4 = 9 => a = 5.

Formula of for sum of first n terms of an AP is

Sₙ = n/2(2a +(n-1)d)

S₄₀ = 40/2(2*5 + (40-1)2) = 20(10+78) = 1760.