The mean of 10 numbers 78, 1010, 1312, 1614, is Answer: 398

Question

The mean of 10 numbers $7	imes8, 10	imes10, 13	imes12, 16	imes14,\ldots$ is

Answer: 398

Accepted Answer

First factors: $7,10,13,\ldots \Rightarrow a_n = 3n+4$. Second factors: $8,10,12,\ldots \Rightarrow b_n=2n+6$.

$T_n = (3n+4)(2n+6) = 6n^2+26n+24$

$$S_{10} = 6\cdot\frac{10\cdot11\cdot21}{6}+26\cdot\frac{10\cdot11}{2}+24\times10 = 2310+1430+240=3980$$

$$\text{Mean} = \frac{3980}{10}=398$$

Solutions · 1