In an ap of n term the sum of first two terms is b and the sum of last two terms is 3 find the sum of its first n term
Answers
Given : In an ap of n term the sum of first two terms is b and the sum of last two terms is 3
To find : sum of its first n term
Solution:
Let say AP is
a , a + d , a + 2d ...................................., a + (n-2)d , a + (n - 1)d
sum of first two terms is b
=> a + a + d = b
=> 2a = b - d Eq1
Sum of last two two terms = 3
=> a + (n - 2)d + a + (n - 1 )d = 3
=> a + (n - 1)d - d + a + (n - 1 )d = 3
=>2 (a + (n-1)d) = 3 + d Eq2
Eq1 + Eq2
=> 2a + 2 (a + (n-1)d) = b - d + 3 + d
=> 2 (a + (a + (n-1) d) = b + 3
=> 2 ( 2a + (n - 1)d ) = b + 3
=> 2a + (n - 1)d = (b + 3)/2
Sum of 1st n terms
= (n/2) (2a + (n-1)d)
= (n/2) ( (b + 3)/2)
= n (b + 3) / 4
Sum of its first n term = n (b + 3) / 4
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