Question

Вычислите пятнадцатый член арифметической прогрессии,если известно,что а1*а4=-32 и а2+а6=16

Answer 1

(a1+d)+(a1+5d)=16        2a1+6d=16       a1+3d=8

a1*(a1+3d)=-32

a1*8=-32

a1=-4                             -4+3d=8

                                       3d=8+4

                                        3d=12

                                           d=4

a15=a1+(15-1)d=-4+14*4=-4+56=52

a15=52

Answer 2

a4=a1+3d

a2=a1+d

a6=a1+5d

$\begin{cases}a1(a1+3d)=-32\\a1+d+a1+5d=16 \end{cases}$

$\begin{cases}(8-3d )(8-3d +3d)=-32\\a1=8-3d \end{cases}$

$\begin{cases}8-3d =-4\\a1=8-3d \end{cases}$

$\begin{cases}d =4\\a1=-4 \end{cases}$ 

a15=a1+14d=-4+14*4=52