Insert 3

Insert five arithmetic progression members between -7 and 3/2.

Correct answer:

a₂ =  -5.5833
a₃ =  -4.1667
a₄ =  -2.75
a₅ =  -1.3333
a₆ =  0.0833

Step-by-step explanation:

$$\begin{gathered} a_1=-7 \\ {a}_7=3\mathrm{/}2={\displaystyle \frac{3}{2}}=1\frac{1}{2}=1.5 \\ {a}_7=a_1+6d \\ d=(a_7-a_1)\mathrm{/}6=(1.5-(-7))\mathrm{/}6={\displaystyle \frac{17}{12}}=1\frac{5}{12}\doteq 1.4167 \\ {a}_2=a_1+d=(-7)+1.4167=-5.5833 \end{gathered}$$

$a_3=a_2+d=(-5.5833)+1.4167=-4.1667$

$a_4=a_3+d=(-4.1667)+1.4167=-2.75$

$a_5=a_4+d=(-2.75)+1.4167=-1.3333$

$a_6=a_5+d=(-1.3333)+1.4167=0.0833$

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