Algebraic definition for the nth term

[livelaughlovee]

I have to determine the next two numbers in the following sequence
and determine an explicit algebraic definition for the nth term.

43, 44, 50, 53, 65, 70, 88, 95, 119, …

I figured out that the next two numbers would be 128 and 158 because the differences between the numbers of the sequence make a pattern. 1, 6, 3, 12, 5, 18, 7, 24. Every other number is odd so the next difference would be 9 and starting with 6 every other number is a multiple of 6.

I just can't figure out how to determine the explicit algebraic definition for the nth term. Can anyone guide me to where I should start?

 

[daon]

looks like you found the key.

If n is even we need to add 6*((n-1)/2)=3(n-1) to the previous number.
If n>1 is odd, we add the (n-1)th odd number to the number before.

\(\displaystyle a_1=43\)
\(\displaystyle a_n = a_{n-1} + (1-n _{\% 2})(n-1) + (n _{\% 2} )[3(n-1)]\)

The "\(\displaystyle n_{\%2}\)" means that we take the remainder of n after dividing by 2. Effectively if n is even this is zero, and if n is odd it is 1.