Question

if AP has 23 terms,the sum of middle three terms is 144 and sum of last three terms is 264. what is 16 term?

Answer 1

Answer:

The middle term is the 12th.  

so, the 11th, 12th and 13th terms have a sum of 144.  

=> (a + 10d) + (a + 11d) + (a + 12d) = 144  

=> 3a + 33d = 144  

i.e. a + 11d = 48.....(1)  

The sum of the last three terms is 264 so,  

(a + 20d) + (a + 21d) + (a + 22d) = 264  

=> 3a + 63d = 264  

i.e. a + 21d = 88.....(2)  

(2) - (1) => 10d = 40, so d = 4 => a = 4  

Then, the 16th term is 4 + 15(4) = 64  

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Answer 2

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