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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.

 Jun 23, 2021
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Sum of arithmetic sequence

 Sum32 =  n/2 ( 2a1 + (n-1)d)

             = 32/2 (2a1  + (32-1)d)

1448    = 16 (2a1 + 31d)

 

 

5th term = 18 = a1 + 4d    so   a1 = 18- 4d     use this value of a1 in the red equation above to calculate 'd'

 

then  ninth term will be:    5th term + 4d  = 18 + 4(d)

 Jun 23, 2021

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