The fifth term of an arithmetic sequence is 18, and the sum of the first 32 terms is \(1448\). Find the ninth term.
18=F + 4D,
1448= 32/2 * [2F + 31D], solve for F, D
Use substitution to get:
F ==196/23 - this is the first term
D==109/46 - this the common difference
9th term ==196/23 + 8*109/46
==196/23 + 872/46
== 632 / 23
Your sequence looks like this:
196 / 23 , 501 / 46 , 305 / 23 , 719 / 46 , 18 , 937 / 46 , 523 / 23 , 1155 / 46 , 632 / 23 , 1373 / 46 , 741 / 23 , 1591 / 46 , 850 / 23 , 1809 / 46 , 959 / 23 , 2027 / 46 , 1068 / 23 , 2245 / 46 , 1177 / 23 , 2463 / 46 , 1286 / 23 , 2681 / 46 , 1395 / 23 , 2899 / 46 , 1504 / 23 , 3117 / 46 , 1613 / 23 , 145 / 2 , 1722 / 23 , 3553 / 46 , 1831 / 23 , 3771 / 46 , >>Number of terms = 32>>Total Sum == 1448
