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The sum of the first four terms of an...

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

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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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