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
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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,…
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