IDNLearn.com provides a user-friendly platform for finding and sharing knowledge. Explore thousands of verified answers from experts and find the solutions you need, no matter the topic.
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.