Question

there are 37 terms in an AP the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429 write the AP​

Answer 1

Answer:

The AP is 3,7,11,15,…

Step-by-step explanation:

The AP has 37 terms.

The middle term is the 19th term.

the middle terms are: (a+17d) 18th term

(a+18d) 19th term &  (a+19d) is 20th term

So the sum of the middle three terms is

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

3a + 54d = 225

a+18d = 75   ____(1)

Similarly the sum of the last three terms  

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

3a+105d = 429

a + 35d = 143  ____(2)

Solving (1) & (2)

17d = 143–75 = 68,

d = 68/17 = 4.

From (1), a = 75–18d

= 75–72 = 3.

So the first term of the AP is 3 and the common difference is = 4. The AP is 3,7,11,15,…

Answer 2

Hope it helps u......!

Answer:;