For a given authentic sequence, the 31st term, a31, is equal to -247, and the 86th term, a86, is equal to-687. find the value of the 9th term a9

We are given 31st term a₃₁ =-247

and a₈₆=-687

The arithmetic sequence formula is given by:

plugging for 31st term , we get

-247= a₁ +(31-1)d

-247=a₁+30d ..............(1)

a₁ = -247-30d........(2)

Plugging for 86th term

-687=a₁ +(86-1)d

-687 =a₁ + 85d ................(3)

Substituting value of a₁ from equation (2) in (3)

-687 = -247-30d +85d

-687 +247 =55d

d=-8

plugging value of d in equation (2)

a₁ = -247-30(-8) = -247 +240 =-7

so first term a₁ =-7 and d=-8

Now we find a₉

a₉ =a₁ +(9-1) d

a₉ = -7 +8(-8) = -71

Answer : a₉ =-71

table 3 represents a direct variation function. : )