An A.P consist of 37 terms. the sum of three middle most term is 225 and the sum of last 3 term is 429. find AP?
Answers
Answered by
7
The middlemost term is (37 + 1) /2 = 19.
Therefore
The three middle most terms are a18 , a19 and a20.
=> a18 + a19 + a20 = 225.
=> a + 17d + a + 18d + a + 19d = 225
=> 3a + 54d = 225
=> a + 18d = 75 ---------eq.1
Last three terms are a35 , a36 and a37.
Therefore
a + 34d + a + 35d + a + 36d = 429.
=> 3a + 105d = 429
=> a + 35d = 143 ----------eq.2
Solving equations 1 and 2
We get
a = 3
d = 4
The AP is 3,7,11,15.........
Therefore
The three middle most terms are a18 , a19 and a20.
=> a18 + a19 + a20 = 225.
=> a + 17d + a + 18d + a + 19d = 225
=> 3a + 54d = 225
=> a + 18d = 75 ---------eq.1
Last three terms are a35 , a36 and a37.
Therefore
a + 34d + a + 35d + a + 36d = 429.
=> 3a + 105d = 429
=> a + 35d = 143 ----------eq.2
Solving equations 1 and 2
We get
a = 3
d = 4
The AP is 3,7,11,15.........
Answered by
0
The three middle terms are T18+T19+T20 is equal to 225
the last 3 terms are T35 + T36 + T37 is equal to 429
A + 17 + A + 18 D + A + 19 b is equal to 225
A + 34d + a+ 35 d+ A + 36 d is equal to 429
substituting the equation is equal to 4 and a is equal to 9 therefore the ap is 9 , 13 , 17 .......
the last 3 terms are T35 + T36 + T37 is equal to 429
A + 17 + A + 18 D + A + 19 b is equal to 225
A + 34d + a+ 35 d+ A + 36 d is equal to 429
substituting the equation is equal to 4 and a is equal to 9 therefore the ap is 9 , 13 , 17 .......
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