The sum of the 3rd and 7th term of an a. p is 6, the product is 8, find the sum of the first 16 terms of the sequence

For starter, recall that an arithmetic progression is given recursively by

We can solve this explicitly for in terms of :

and so on, down to

More generally, we can express in terms of an arbitrary term :

(notice how the index of and the coefficient of on the right side add to )

Let be the -th term of this particular progression. We're given

from which it follows that

If , it follows that

Otherwise, if , then

The sum of the first terms of an arithmetic progression is

If , then

so that

Otherwise, if , then

so that

all about the same size in the city the game was

step-by-step explanation: