Caclulating the sum between two known intergers assuming constant growth between them

Hi all,

This is related to my work (deadline is imminent and help woudl be greatly appreciated!). I imagine there is an easy answer but I have been unable to find it.

I have traffic counts for two years 2017 and 2032. Assuming a constant growth between these two dates, can i calculate the sum of all the values between these two years (i.e. the total number of vehciles passing during this time period).

2014 - 17 HGV's
2032 - 29 HGV's

2014 - 195 HGV's
2032 - 396 HGV's

There is a yearly increase in vehciles between 2017 and 2032. the increase in vehciles in linear growth.
i want to know the TOTAL number of vehicles on the road between 2017 and 2032.
I could do this by calculating a yearly increase and making a table then summing the results but that is time consuming and not effective. I would rather use a formula.
So;
the formula needs to sum all of the, at present, unknown intergers between the two years.

the long way is like this:

2017 17
2018 29
2019 41
2020 53
2021 65
2022 77
2023 89
2024 101
2025 113
2026 125
2027 137
2028 149
2029 161
2030 173
2031 185
2032 197


Sum of column 2 to get answer = 1712

But; if I only know the first and last value, is there a quick way to calculate the sum of all the itermediate values without having to write all of it out?

Thanks

p.s. thanks to everyone who posts on here, your advice has saved me a number of times (yes that may be a little buttering up but it is true!!)