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The sum of first four terms of an A.P. i...

The sum of first four terms of an A.P. is 56 and the sum of it's last four terms 112. If its first term is 11 then find the number of terms in the A.P

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`a + a + d + a + 2d + a + 3d = 56`
`4a + 6d = 56`
`44 + d = 56` (as a = 11)
`6d = 12` hence d = 2
Let total number of terms = n
Now sum of last four terms
`a + (n - 1) d + a + (n - 2) d + a + (n - 3) d + a + (n - 4) d = 112`
`rArr 4a + (4n - 10) d = 112 " " rArr 44 + (4n - 10)2 = 112`
`rArr 4n - 10 = 34`
`rArr n = 11`
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