Question

if 7 times the 7th term of an AP is equql to 11 times the 11th term of an AP then what will be the value of a18*a19

Answer 1

Answer:

0

Step-by-step explanation:

The 7th term is a₇ = a + 6d ----------(1)

The 11th term is a₁₁ = a + 10d ----------(2)

By condition,

7(a₇) = 11(a₁₁)

∴ 7(a + 6d) = 11(a + 10d)

7a + 42d = 11a + 110d

∴ -4a = 68d

∴ a = -17d

Substitue a in (1) and (2)

∴ a₇ = -17d + 6d = -11d      

  a₁₁ = -17d + 11d = -6d

Given a₁₈ x a₁₉:

a₁₈ = a + 17d = -17d + 17d = 0

a₁₉ = a + 18d = -17d + 18d = -d

a₁₈ x a₁₉ = 0 x -d = 0

∴ a₁₈ x a₁₉ = 0

Hope this helps!