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Sagot :
In the given sequence, we have an arithmetic sequence which is given by the following formula:
[tex]a_n=a_1+(n-1)d[/tex]Where an is the nth term of the sequence, a1 is the first term, n is the number of terms and d is the common difference.
We can find the common difference by applying the formula:
[tex]d=a_n-a_{n-1}[/tex]If we replace an=-22 and an-1=-30, we find:
[tex]\begin{gathered} d=-22-(-30) \\ d=-22+30 \\ d=8 \end{gathered}[/tex]The common difference is d=8.
The number that goes in the green box is the 6th term of the sequence. Then a1=-30, n=6, d=8. Replace these values into the formula and solve:
[tex]\begin{gathered} a_6=-30+(6-1)\cdot8 \\ a_6=-30+(5)\cdot8 \\ a_6=-30+40 \\ a_6=10 \end{gathered}[/tex]The answer is 10.
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