Question

The first term of a certain sequence is -2 and the second term is -4. Every term after the second term is obtained by dividing the sum of the previous two terms by 2. What is the sixth term of the sequence?
I get the general way of doing this but is there a sequence formula to it and if so what is it?

Answer 1

its a triangle:D

Answer 2

if 1 term is a, next is b
then 3rd is (a+b)/2
after that (a+2b)/4
then (2a+3b)/8
then (3a +5b)/16
so you see,,from the 4th term onwards, coefficients of a and b increase as a fibonacci series/
and denominator is 2^n

Answer 3

so i'm assuming that if i were to plug in -2 as a and -4 as b in (3a+5b)/16 i would get the correct answer?

Answer 4

\[\Large -2,-4,-3,-3.5,-3.25,\dots\]

Answer 5

the fourth term is:\[\Large {b+{a+b \over 2}\over 2}={a+3b \over 4}\]

the fifth term is:\[\Large {{a+3b \over 4}+{a+b \over 2}\over 2}={3a+5b \over 8}\]......

Answer 6

when i plug in its close but not the exact answer as it would be for -27/8