two terms of an arithmetic sequence are a6 = 40 and a20 = - 16. write and explicit rule for the nth term

Tn = 64-4n

Step-by-step explanation:

The nth term of an AP is expressed as:

Tn = a + (n-1) d

a is the common difference

n is the number of terms

d is the common difference

Given the 6th term a6 = 40

T6 = a + (6-1) d

T6 = a+5d

40 = a+5d ... (1)

Given the 20th term a20 = - 16

T20 = a + (20-1) d

T20 = a+19d

-16 = a+19d ... (2)

Solving both equation simultaneously

40 = a+5d

-16 = a+19d

Subtracting both equation

40 - (-16) = 5d-19d

56 = - 14d

d = 56/-14

d = - 4

Substituting d = - 4 into equation

a+5d = 40

a+5 (-4) = 40

a-20 = 40

a = 20+40

a = 60

Given a = 60, d = - 4, to get the nth term of the sequence:

Tn = a + (n-1) d

Tn = 60 + (n-1) (-4)

Tn = 60 + (-4n+4)

Tn = 60-4n+4

Tn = 64-4n