The mean of 10 numbers $7 imes 8,10 imes 10,13 imes 12,16 imes 14, \ldots$. is

Question

The mean of 10 numbers $7 	imes 8,10 	imes 10,13 	imes 12,16 	imes 14, \ldots$. is

Professor PC Thomas Classes · Answer

(398) : We have, $7 	imes 8,10 	imes 10$,\ $13 	imes 12,16 	imes 14, \ldots$\ Clearly, $n^{	ext {th }}$ term of given series,\ $t_{n}=(7+(n-1) \cdot 3)(8+(n-1) \cdot 2)$\ $=6 n^{2}+26 n+24$\ Now, $\sum_{n=1}^{10} t_{n}$\ $=10 	imes 11 	imes 21+13 	imes 10 	imes 11+240=3980$\ $	herefore$ Required mean $=\frac{3980}{10}=398$\