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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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: $a}_{n+1}={a}_{n}+d\to d={a}_{n+1}-{a}_{n$

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.

Thus if $a}_{1$ in the first term, ${a}_{2}={a}_{1}+d$

In general: $a}_{n+1}={a}_{n}+d\to d={a}_{n+1}-{a}_{n$

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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