EXPLANATION.
8th term of an A.P. is double the 13th term.
To prove : 2nd term is double the 10th term.
As we know that,
General term of an A.P.
⇒ Tₙ = a + (n - 1)d.
Using this formula in this question, we get.
8th term of an A.P. is double the 13th term.
⇒ T₈ = 2 x T₁₃.
⇒ a + (8 - 1)d = 2 x [a + (13 - 1)d].
⇒ a + 7d = 2 x [a + 12d].
⇒ a + 7d = 2a + 24d.
⇒ a - 2a = 24d - 7d.
⇒ - a = 17d.
⇒ a = - 17d.
2nd term is double the 13th term.
⇒ T₂ = a + (2 - 1)d.
⇒ T₂ = a + d.
Put the values in the expression, we get.
⇒ T₂ = - 17d + d.
⇒ T₂ = - 16d.
Double the 13th term.
⇒ 2 x T₁₃.
⇒ 2 x [a + (13 - 1)d].
⇒ 2 x [a + 12d].
⇒ 2a + 24d.
⇒ 2(-17d) + 24d.
⇒ - 34d + 24d.
⇒ - 10d.
No, 2nd term is not equal to double the 13th term.
Hence, 2nd term is equal to double the 10th term.