Mathematics
In an A.P., eight times of 8th term is equal to fifteen times the fifteenth term. Find the 23rd term of the A.P.
AP GP
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Answer
Let first of A.P. be a and common difference be d.
By formula,
an = a + (n - 1)d
Given,
Eight times of 8th term is equal to fifteen times the fifteenth term.
⇒ 8a8 = 15a15
⇒ 8[a + (8 - 1)d] = 15[a + (15 - 1)d]
⇒ 8[a + 7d] = 15[a + 14d]
⇒ 8a + 56d = 15a + 210d
⇒ 15a - 8a = 56d - 210d
⇒ 7a = -154d
⇒ a = -
⇒ a = -22d
⇒ 22d = -a.
a23 = a + (23 - 1)d
= a + 22d
= a - a
= 0.
Hence, 23rd term of A.P. = 0.
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