SOLUTION: The 6th term of Ap is 35 and the 13th term is 77. find the 20th term

There are 13 - 6 = 7  intervals (gaps)  between the 6th and 13th terms of the AP.


Therefore, the width of each gap is   =  = 6.


It means that the common difference of the arithmetic progression is 6.


Next, there are  20-13 = 7 intervals (gaps) between the 13th and 20th terms;


therefore, the 20th term is   + 7*6 = 77 + 42 = 119.


ANSWER.  The 20th term is 119.

Another possible solution is to notice that the 13th term of an AP is exactly half of the way between the 6th and 20th terms
(the midpoint).


It means that the distance from the 13th term to the 20th term is exactly the same as between the 6th term and 13th term
which is 77-35 = 42.


Therefore, we add 42 to 77 and obtain the 20th term as  77+42 = 119,  getting the same answer.