Let form an arithmetic sequence. What is the sixth term of this sequence?

171/40 or 4 11/40

Step-by-step explanation:

AP givena + b, a - b,  ab, a/bTo find6th termSolution

Common difference

Difference of first two

d = (a -b) - (a + b) = -2b

Difference of second two

d= ab - (a - b)

Difference of last two

d = a/b - ab

Now comparing d:

-2b = ab - (a - b)ab - a = - 3ba(1 - b) = 3ba = 3b/(1 - b)

and

a/b - ab = -2ba(1/b - b) = -2ba = 2b²/(b² - 1)

Eliminating a:

2b²/(b² - 1) = 3b/(1 - b)2b/(b+1) = -32b = -3b - 35b = - 3b = -3/5

Finding a:

a = 3b/(1 - b) = 3*(-3/5) *1/(1 - (-3/5)) = -9/5*5/8 =-9/8

So the first term is:

a + b = -3/5 - 9/8 = -24/40 - 45/40 = - 69/40

Common difference:

d = -2b = -2(-3/5) = 6/5

The 6th term:

a₆ = a₁ + 5d =-69/40 + 5*6/5 = -69/40 + 240/40 =171/40 = 4 11/40