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Question
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
Options
- \[\frac{ab}{2(b - a)}\]
- \[\frac{ab}{(b - a)}\]
- \[\frac{3ab}{2(b - a)}\]
none of these
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Solution
In the given problem, we are given first, second and last term of an A.P. We need to find its sum.
So, here
First term = a
Second term (a2) = b
Last term (l) = 2a
Now, using the formula an = a+ ( n - 1) d
a2 = a + (2 - 1)d
b = a + d
d = b - a ......(1)
Also,
an = a + (n-1) d
2a = a + nd - d
2a - a = nd - d
`(a + d)/d = n ` ...........(2)
Further as we know,
`S_n = n/2 [ a + l]`
Substituting (2) in the above equation, we get
Using (1), we get
`S_n = ( a + (b - a) )/(2(b - a)) (3a) `
`S_n =b / ( 2 ( b-a) ) (3a)`
Thus,
`S_n = (3ab)/(2(b-a))`
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