Question

If 6 times of 6th term of an A.P. is equal to 7 times the 7th term, then the 13th
term of the A.P. is

Answer 1

EXPLANATION.

→ 6th times the 6th term of an Ap equal to

7 times the 7th term.

→ Then find the 13th term of an Ap.

→ Nth term of an Ap.

→ An = a + ( n - 1 ) d

→ 6(T6) = 7(T7)

→ 6 ( a + 5d ) = 7 ( a + 6d )

→ 6a + 30d = 7a + 42d

→ a = -12d .....(1)

→ 13th term of an Ap.

→ T13 = a + 12d

→ put the value of equation (1) in T13th term.

→ -12d + 12d = 0

→ Therefore,

→ 13th term of an Ap = 0.

Answer 2

║⊕ANSWER⊕║

=> 6(ᴀ+5ᴅ) = 7(ᴀ+6ᴅ)

=> 6ᴀ+30ᴅ = 7ᴀ+42ᴅ

=> 6ᴀ-7ᴀ = 42ᴅ-30ᴅ

=> -ᴀ = 12ᴅ

=> -ᴀ-12ᴅ = 0

=> a13 = -12d + 12 d = 0