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

charlygyloavao9

charlygyloavao9

Answered question

2022-10-05

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

Answer & Explanation

Yasminru

Yasminru

Beginner2022-10-06Added 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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