Question

an AP consists of 37 terms . Sum of 3 middlemost terms is 225 sum of last 3 terms is 429. find AP

Answer 1

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A.P consist of 37 terms.

Middle Term = (37 + 1)/2

=> 38/2. = 19th term.

Therefore, The three middle term is 18th term, 19th term and 20th term.

A.T.Q.

a 18 + a19 + a20 = 225

=> (a + 17d) + (a + 18d) + (a + 19d) = 225

=> 3a + 54 = 225

=> 3( a + 18d) = 3( 75)

=> a + 18d = 75

=> a = 75 - 18d ---------------(1).

Sum of Last three term = 429

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

⇒ 3(a + 35d) = 429

⇒ (75 – 18d) + 35d = 143

⇒ 17d = 143 – 75 = 68

⇒ d = 4

Substituting the value of d in equation (1), it is obtained

a = 75 – 18 × 4 = 3

Thus, the A.P. is 3, 7, 11, 15,.......
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