in an ap sum of first two terms is 5 and sum of last two terms is 129 then find the sequence
Answers
Given : in an ap sum of first two terms is 5 and sum of last two terms is 129
To find : Sequence
Solution:
Let say first two terms
a , a + d
and last two terms
L , L - d
a + a + d = 5
L + L - d = 129
Adding both
2a + 2L = 134
=> a + L = 67
2L - 2a - 2d = 124
=> L - a - d = 62
=> L = 62 + a + d
a + (n-1)d = 62 + a + d
=> (n - 2)d = 62
62 = 1 * 62 or 2* 31
4 possible cases
d = 1 using a + a + d = 5 => a = 2
n = 64
Sequence is 2 , 3 , 4 ........................., 64 , 65
d = 2 using a + a + d = 5 => a = 1.5
1.5 , 3.5 , ................................ 63.5 , 65.5
d = 31 => a = - 13
-13 , 18 , 49 , 80
d = 62 => a = - 28.5
-28.5 , 33.5 , 95.5
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