Question

an arithmetic progression has 37 terms the sum of the middle term and the two terms adjacent one on either side to it is 225 if the sum of the lasrt 3 terms is 429 . find the first three term's of A.P

Answer 1

the answer for your question is with attachment

Answer 2

Answer:

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Step-by-step explanation:

Let the first term and the common difference of an AP are a & d respectively.

Since the AP contains 37terms . So,the Middle most Term is (37+1)/2th term

= 19th Term

Thus,Three most Middle Terms ⇒ 18th , 19th & 20th

Given $a_{18} + a_{19} + a_{20}$ = 225

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

⇒ 3(a + 18d) = 225

⇒ a + 18d = 75

⇒ a + 75 - 18d...... ( i )

According for the giving Information

$a_{35}+ a_{36}+ a_{37}$  = 429

⇒ (a + 34d) + (a + 35d) + (a + 37d) = 429

⇒ 3(a + 35d) = 429

⇒ (75 - 18d) + 35d = 143

⇒ 17d = 148 - 75 = 68

⇒ d = 4

Substituting the value of eq (1) , it is obtained

a = 75 - 18 x 4 = 3

Thus , The AP is 3, 7 , 11 , 15.....