if 5 times the 5th term of an A. P is equal to 8 times the 8th term show that it 13th term is zero
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Let a and d be the first term and common difference of A.P.
Given, 5a 5 = 8 a 8
5 (a + 4d) = 8(a + 7d) (an = a + (n – 1) d)
5a + 20d = 8a + 56d
5a – 8a = 56d – 20d
–3a = 36d
a = –12d … (1)
a 13 = a + 12d = –12d + 12d = 0 (Using (1)) therefore a 13=0
Given, 5a 5 = 8 a 8
5 (a + 4d) = 8(a + 7d) (an = a + (n – 1) d)
5a + 20d = 8a + 56d
5a – 8a = 56d – 20d
–3a = 36d
a = –12d … (1)
a 13 = a + 12d = –12d + 12d = 0 (Using (1)) therefore a 13=0
kamal521386:
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