We are given 31st term a₃₁ =-247
and a₈₆=-687
The arithmetic sequence formula is given by:
[tex] a_{n} =a_{1} +(n-1)d [/tex]
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
