Question

10 times the 10th term and 15 times the 15th term of an A.P. are equal. Find the 25th term of this A.Р.

Answer 1

The formula for the n^th term of an Arithmetic Progression is 𝑎_𝑛 = 𝑎 + (𝑛 − 1)𝑑.

10 × a₁₀ = 15 × a₁₅

Substitute the term formulas:

10(a + 9d) = 15(a + 14d)

Divide both sides by 5:

2(a + 9d) = 3(a + 14d)

2a + 18d = 3a + 42d

Rearrange the terms to one side:

3a − 2a + 42d − 18d = 0

a + 24d = 0

The formula for the 25th term (a₂₅) is:

a₂₅ = a + (25 − 1)d

a₂₅ = a + 24d

a + 24d = 0

a₂₅ = 0