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Question
The sum of 15 terms of an A.P. is zero, and its 5th term is 12. Find its 12th term.
Sum
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Solution
`S_n = n/2[2a + (n - 1)d]`
`S_15 = 15/2[2a + (15 - 1)d]`
2a + 14d = 0
2a = −14d
a = `(−14d)/2`
a = −7d
an = a + (n − 1)d
an = a + (5 − 1)d
a + 4d = 12
−7d + 4d = 12
−3d = 12
d = `12/-3`
d = −4
a = −7d
a = (−7) × (−4)
a = 28
a12 = a + (n − 1)d
= 28 + (12 − 1)(−4)
= 28 + 11 × (−4)
= 28 − 44
= −16
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