Sherman has two sequences . The first sequence is described by the explicit rule f(n) = 15n + 4 and the second sequence is described by the explicit rule f(n) = 4n + 15 . Find the sum of the 20th term in each sequence . The sum of the 20th term in each sequence is

Step-by-step explanation:

Given the explicit function as

f(n) = 15n+4

The first term of the sequence is at when n= 1

f(1) = 15(1)+4

f(1) = 19

a = 19

Common difference d = f(2)-f(1)

f(2) = 15(2)+4

f(2) = 34

d = 34-19

d = 15

Sum of nth term of an AP = n/2{2a+(n-1)d}

S20 = 20/2{2(19)+(20-1)15)

S20 = 10(38+19(15))

S20 = 10(38+285)

S20 = 10(323)

S20 = 3230.

Sum of the 20th term is 3230

For the explicit function

f(n) = 4n+15

f(1) = 4(1)+15

f(1) = 19

a = 19

Common difference d = f(2)-f(1)

f(2) = 4(2)+15

f(2) = 23

d = 23-19

d = 4

Sum of nth term of an AP = n/2{2a+(n-1)d}

S20 = 20/2{2(19)+(20-1)4)

S20 = 10(38+19(4))

S20 = 10(38+76)

S20 = 10(114)

S20 = 1140

Sum of the 20th terms is 1140