Write the expression we could use for the nth term of the ar

Write the expression we could use for the nth term of the arithmetic sequence -19, -14, -9, -4, 1, .... Use that equation to find A subscript 36 and S subscript 36 . Show all work

Solution

S= -19 , -14 , -9 , -4 .....

common difference = -14 -(-19) = 5

a1 = -19

nth term = a1 +(n-1)d = -19 + (n-1)5 = -19 +5n -5 = 5n -24

36 th term = 5*36 -24 = 156

Sum(36 term) = (n/2)[2a + (n-1)d] = (36/2)[ 2*-19 + (36 -1)5 ]

=18[ -38 + 175]

=2466