If thrice the third term of an A.P. ,equal to 5 times its fifth term. then show that 8th term is zero.
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Third term of an AP, A3 = a + 2d
Fifth term of an AP., A5 = a + 4d
According to the question,
3 [ a + 2d ] = 5 [ a + 4d ]
3a +6d = 5a + 20d
5a - 3a = 6d - 20d
2a = - 14 d
a = ( - 14 /2 ) d
a = - 7d
Eighth term of the AP, A8 = a +7d
A8 = - 7d +7d = 0
Hence, 8th term of the AP is 0.
Proved.
Fifth term of an AP., A5 = a + 4d
According to the question,
3 [ a + 2d ] = 5 [ a + 4d ]
3a +6d = 5a + 20d
5a - 3a = 6d - 20d
2a = - 14 d
a = ( - 14 /2 ) d
a = - 7d
Eighth term of the AP, A8 = a +7d
A8 = - 7d +7d = 0
Hence, 8th term of the AP is 0.
Proved.
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