Question

The sum of the 1st nine terms of an arithmetic series is 216. The 1st,3rd and the 7th terms of series form the 1st three terms of a geometric series. Find the 1st term and the constant difference of the arithmetic series ?

Answer 1

just write what they told you:

9/2 (2a+8d) = 216
(a+2d)/(a) = (a+6d)/(a+2d)

Now solve for a and d.

Now, just for precision, you mean arithmetic sequence. A series is the <i>sequence of partial sums</i> of a sequence. For example,

sequence: 3,7,11,15,19,...
series: 3,10,21,36,55,...

Answer 2

The third term of an arithmetic sequence is 14 and the ninth term is -1 find the first four term of the sequence