Question

Number of terms in an arithmetic progression is \(2n\). Sum of terms occurring at even places is 40 and sum of terms occurring at odd places is 55. If the first term exceeds the last term by 27, then \( n \) equals to:

Answer 1

Let the first term of the arithmetic progression be \( a \) and the common difference be \( d \). - The sum of the terms occurring at even places: \[ S_{\text{even}} = n \left( a + (2n-2)d \right) = 40. \] - The sum of the terms occurring at odd places: \[ S_{\text{odd}} = n \left( a + (2n-1)d \right) = 55. \] From the given information, we also know that the first term exceeds the last term by 27, which gives the equation: \[ a - \left( a + (2n-1)d \right) = 27. \] Solving this system of equations will give the value of \( n \).