Arithmetic 81808

An increasing arithmetic sequence has an odd number of terms. The middle term is 302. If we remove the 4 largest terms from the sequence, the middle term will be 296. Determine the difference in the sequence.

Correct answer:

d =  3

Step-by-step explanation:

$$\begin{gathered} d>0 \\ a+d\cdot (n+1)/2=302 \\ a+d\cdot (n-4+1)/2=296 \\ n=4+4+1=9 \\ a+d\cdot (n+1)/2=302 \\ a+d\cdot (n-4+1)/2=296 \\ a+d\cdot (9+1)/2=302 \\ a+d\cdot (9-4+1)/2=296 \\ 2a+10d=604 \\ 2a+6d=592 \\ Row2-Row1\to Row2 \\ 2a+10d=604 \\ -4d=-12 \\ d=\frac{-12}{-4}=3 \\ a=\frac{604-10d}{2}=\frac{604-10\cdot 3}{2}=287 \\ a=287 \\ d=3 \end{gathered}$$

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