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Answer:
-125
Step-by-step explanation:
Each term is 7 less than the previous term.
1st term: 15
2nd term: 15 - 7
3rd term: 15 - 7 - 7 = 15 - 2(7)
4th term = 15 - 7 - 7 - 7 = 15 - 3(7)
Notice that each term is 15 minus a multiple of 7. The multiple is obtained by multiplying 7 by 1 less than the term number.
The formula is:
[tex] a_n = 15 - 7(n - 1) [/tex]
For the 21st term, multiply 7 by 20, and subtract from 15.
7 × 20 = 140
15 - 140 = -125
Using the formula:
[tex] a_{21} = 15 - 7(21 - 1) = 15 - 7(20) = 15 - 140 = -125 [/tex]
Answer: -125