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Answer:
The 50th term of the sequence that begins with - 6 is 288.
Step-by-step explanation:
Definition of Arithmetic Progression
An arithmetic progression, also known as an arithmetic sequence, is a set of numbers in which the difference between successive terms remains constant. The sequence 5, 7, 9, 11, 13, 15,... is, for example, an arithmetic progression with a common difference of 2.
Formula -[tex]$a_{n}=a_{1}+(n-1) d$[/tex]
The given sequence is − 6, 0, 6, 12,
It is in arithmetic progression as the common difference between all consecutive numbers is 6.
Let a1 be the first term and d be the common difference.
Therefore, a1 = - 6 and d = 6
For 50th term, a50 = a1 + (n - 1) d
= - 6 + (50 - 1) 6
= - 6 + 49 × 6
= - 6 + 294
= 288
Thus, the 50th term of the sequence is 288.
Learn more about arithmetic progression here-https://brainly.com/question/24462795
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