The ninth term of an arithmetic progression is 20. what is the sum of its 17 members?

Let us denote by a1 and a9 the members of this arithmetic sequence, which are at positions number one and number nine, respectively, and by d – the difference of this arithmetic sequence.

In the initial data for this task, it is reported that the a9 term is equal to two tens, therefore, the following relationship takes place:

a9 = a1 + (9 – 1) * d = a1 + 8d = 20.

Let’s find the sum of the members of this arithmetic progression from the first to the 17th inclusive:

S7 = (2 * a1 + d * (17 – 1)) * 17/2 = (2 * a1 + d * 16) * 17/2 = 2 * (a1 + d * 8) * 17/2 = (a1 + 8d) * 17 = a9 * 17 = 20 * 17 = 340.

Answer: the required amount is 340.