If , and are in AP and ⁻¹ , ⁻¹ and ⁻¹ are also in AP, then

Step-by-step solution

Since, , and are in AP. 2 = + ...(i) Also, ⁻¹ , ⁻¹ and ⁻¹ are also in AP. array lrl & 2 ⁻¹ & = ⁻¹ + ⁻¹ & ⁻¹ ( 2 1- ^2 ) & = ⁻¹ ( + 1- ) & 2 1- ^2 & = + 1- & + 1- ^2 & = + 1- ｂy using & ^2 & = array [by using Eq. (i)] Since, , and are in AP as well as in GP. = =