Question

If the first and the (2n - 1 )th term of an AP, GP and HP are equal and their nth terms are a,b and c respectively, then  

(a) a = b = c 

(b) a ≥ b ≥ c 

(c) a + c = b 

(d) ac - b² = 0

Answer 1

The correct option is 

(a) a = b = c 

(b) a ≥ b ≥ c 

(d) ac - b² = 0

Explanation:

Since, first and (2n - 1)th terms are equal. Let first term be x and (2n - 1)th term be y. Whose middle term is t_n

Here, equatity holds (ie, a = b = c) only if all terms are same. 

Hence, option (a), (b) and (d) are correct.