Question

what is the next term in series 832.5,810,790,772.5,757.5,?

Answer 1

This is simple series .
Let see how ,
Given, 832.5, 810, 790 , 772.5 , 757.5 , ?
832.5 - 22.5 = 810
810 - (22.5 - 1 × 2.5) = 810 - 20 = 790
790 - (22.5 - 2 × 2.5) = 790 - 17.5 = 772.5
772.5 - (22.5 - 3 × 2.5) = 772.5 - 15 = 757.5
757 - (22.5 - 4 × 2.5) = 757.5 - 12.5 = 745

Hence, answer is 745

Answer 2

In the observation, it is clear that
the differences of terms of the above
sequence are not equal.

But the differences form an AP.

t2 - t1= 810 - 832.5= - 22.5

t3 - t2 = 790 - 810 = -20

t4 - t3 = 772.5 - 790 = - 17.5

t5 - t4 = 757.5 - 772.5 = - 15

so the next difference must be

t6 - t5 = - 12.5

===> t6 = t5 - 12.5

t6 = 757.5 - 12.5 = 745

Next term is 745

I hope this answer helps you