Question

4. Find the first three terms of the arithmetic series. Remember to use the formula S, - (Q, +a,) to find n, and the formula a, - az + (n − 1)d to find'd.9,- -2,a, - -54, 5, --392O -54 +-50 + -46 + ...0-2 +-6 + -10 + ..0-2 +-56 + -110 +0-2 +2 +6+

Answer 1

To answer this question we will substitute the given values into the formulas to compute n and d.

Substituting Sₙ=-392, a₁=-2, and aₙ=-54 in the first formula we get:

`-392=(n)/(2)(-2+(-54)).`

Simplifying the above result we get:

`\begin{gathered} -392=(n)/(2)(-56), \\ -392=-28n. \end{gathered}`

Dividing the above equation by -18 we get:

`\begin{gathered} (-392)/(-18)=(-18n)/(-18), \\ 14=n. \end{gathered}`

Now, substituting n=14, aₙ=-54, and a₁=-2 in the second formula we get:

`-54=-2+(14-1)d.`

Simplifying the above result we get:

`-54=-2+13d.`

Then:

`\begin{gathered} -52=13d, \\ -4=d. \end{gathered}`

Now, using the second formula, a₁=-2, and d=-4 we get:

`\begin{gathered} a_2=-2+(2-1)(-4)=-2+(-4)=-6, \\ a_3=-2+(3-1)(-4)=-2+2(-4)=-10. \end{gathered}`

Therefore the first three terms of the arithmetic series are:

`-2+-6+-10+\cdots`

Answer: Second option.