Question

In a certain ap the 24 term is twice the 10 term . prove that the 72 nd term is twice the 34term

Answer 1

$\underline{ \large{ \text{Answer}}} : \\ \\ \text{Let, the first term of the AP is a and the} \\ \text{common difference is d.} \\ \\ \text{By the given condition, we have -} \\ \text{24th term} = 2 \times \text{10th term} \\ \to \text{a + 23d = 2 (a + 9d)} \\ \to \text{a + 23d = 2a + 18d} \\ \to \text{2a - a = 23d - 18d} \\ \to \text{a = 5d} \\ \\ \text{Now, 72nd term = a + 71d} \\ \text{ = 5d + 71d = 76d and} \\ \text{34th term = a + 33d} \\ \text{ = 5d + 33d = 38d} \\ \\ \implies \boxed{\text{72nd term = 2(34th term)}} \\ \\ \bigstar \underline{ \large{ \text{MarkAsBrainliest}}} \bigstar$