Find the sum of all 11 terms of an ap
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Find the sum of the 11th terms of an AP .whose middle term is 30.
Answered by admin @
Answer:
330
Step-by-step explanation:
We know for odd term :
Middle term = [ ( n + 1 ) / 2 ]th term :
Given n = 11 :
Middle term = ( 11 + 1 ) / 2 = 6th
We have value of t₆ = 30 :
t_n = a + ( n - 1 ) d
= > t₆ = a + ( 6 - 1 ) d
= > 30 = a + 5 d
= > a = 30 - 5 d ..... ( i )
We know for sum of A.P. :
S_n = n / 2 ( 2 a + ( n - 1 ) d ) )
S₁₁ = 11 / 2 ( 2 a ( 11 - 1 ) d )
Using ( i ) we get :
S₁₁ = 11 / 2 ( 60 - 10 d + 10 d )
S₁₁ = 11 × 30
S₁₁ = 330
Therefore , sum of 11th terms is 330.
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