An AP consists of 37 terms. The sum of the three middle most terms is 225 and the

sum of the last three is 429. Find the AP.

Here is the answer to your question.

Let the first term and the common difference of the A.P are

*a*and*d*respectively.Since the A.P contains 37 terms. So, the middle most term is (37+1)/2 th term = 19

^{th}term.Thus, three middle most terms of this A.P.are 18

^{th}, 19^{th}and 20^{th}terms.Given

*a*_{18}+*a*_{19}+*a*_{20}= 225⇒ (

*a*+ 17*d*) + (*a*+ 18*d*) + (*a*+ 19*d*) = 225⇒ 3(

*a*+ 18*d*) = 225⇒

*a*+ 18*d*= 75⇒

*a*= 75 – 18*d*… (1)According to given information

*a*

_{35}+

*a*

_{36}+

*a*

_{37}= 429

⇒ (

*a*+ 34*d*) + (*a*+ 35*d*) + (*a*+ 36*d*) = 429⇒ 3(

*a*+ 35*d*) = 429⇒ (75 – 18

*d*) + 35*d*= 143⇒ 17

*d*= 143 – 75 = 68⇒

*d*= 4Substituting the value of

*d*in equation (1), it is obtained*a*= 75 – 18 × 4 = 3

Thus, the A.P. is 3, 7, 11, 15 …

Hope! This will help you.

Cheers!

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