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The fifth term of an arithmetic sequence is 18, and the sum of the first 32 terms is 1448. Find the ninth term.

 May 24, 2022
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18 ==F  +  4D............................(1)

1448 ==32 / 2 * [2F + 31D......(2), solve for D, F

 

F==196 / 23 - this is the first term

D ==109 /46 - this is the common difference.

 

Your sequence looks like this:

 

8.52173913 , 10.89130435 , 13.26086957 , 15.63043478 , 18 , 20.36956522 , 22.73913043 , 25.10869565 , 27.47826087 , 29.84782609 , 32.2173913 , 34.58695652 , 36.95652174 , 39.32608696 , 41.69565217 , 44.06521739 , 46.43478261 , 48.80434783 , 51.17391304 , 53.54347826 , 55.91304348 , 58.2826087 , 60.65217391 , 63.02173913 , 65.39130435 , 67.76086957 , 70.13043478 , 72.5 , 74.86956522 , 77.23913043 , 79.60869565 , 81.97826087 , >>Number of terms = 32>>Total Sum == 1448

 

The 9th term ==632 / 23 ==27.47826087

 May 24, 2022

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