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.

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Let first of A.P. be a and common difference be d.

By formula,

a_n = 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 = - $\dfrac{154d}{7}$

⇒ 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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