Tell whether the sequence 2, -5, -12, -19, -26 is arithmetic

charlygyloavao9 2022-10-05 Answered
Tell whether the sequence 2, -5, -12, -19, -26 is arithmetic
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Answers (1)

Yasminru
Answered 2022-10-06 Author has 6 answers
For a sequence to be arithmetic all consecutive terms must differ by a fixed amount (d) called the common difference.
Thus if a 1 in the first term, a 2 = a 1 + d
In general: a n + 1 = a n + d d = a n + 1 - a n
In our sequence: 2,−5,−12,−19,−26
a 1 = 2
a 2 = - 5
If the sequence is to be arithmetic: d=−5−2=−7
Testing the next terms in tern:
a 3 = - 5 - 7 = - 12 Correct
a 4 = - 12 - 7 = - 19 Correct
a 5 = - 19 - 7 = - 26 Correct
Since all terms satisify the general condition, the sequence is arithmetic.
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