This is the same thing as being asked to find the 14^{th} partial sum of {*a*_{n}} = -4*n* + 20. All we need to do to evaluate this partial sum is to find the number of terms as well as the first and last terms. a_{1 }= -4(1) + 20 = 16
*a*_{2 }= -4(2) + 20 = 12
*a*_{3 }= -4(3) + 20 = 8 So start by listing the first few terms to find the first term and common difference, *d*. *a*_{1 }= 16
*d* = – 4
Identify the first term and common difference between each term from the list. *a*_{14} = -4(14) + 20
*a*_{14} = - 36
Use the given rule to find the 14^{th} term by plugging 14 in for *n.*
Use the formula for a partial sum of an arithmetic series and simplify to find your final solution. |