he298c

2020-10-18

Determine whether the given sequence is arithmetic.
If so, then find the common difference.
$4,9,14,19,24,...$

bahaistag

Skilled2020-10-19Added 100 answers

From the above sequence, it can be observed that ${a}_{1}=4,{a}_{2}=9,{a}_{3}=14,{a}_{4}=19,{a}_{5}=24.$
Subtract the two consecutive numbers of the sequence as shown below:
${a}_{2}-{a}_{1}=9-4$

$=5$

$a3-a2=14-9$

$=5$

${a}_{4}-{a}_{3}=19-14$

$=5$

${a}_{5}-{a}_{4}=24-19$

$=5$
It can be seen that the difference between the two consecutive numbers of the sequence is 5 (a constant). Thus, the given sequence is arithmetic and the common difference is 5.

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