emancipezN

2021-02-23

Determine whether the sequence is arithmetic. If so, identify the common difference 11, 10.2, 9.4, 8.6, 7.8, …

Layton

Step 1
For a sequence to be an arithmetic progression it must follow the common difference procedure as.
$a,b,c,d,e,.....$
$b-a=c-b=d-c=e-d=....$
Step 2
For the given sequence, check whether it follows the common difference as suggested above.
$11,10.2,9.4,8.6,7.8,....$
$10.2-11=-0.8$
$9.4-10.2=-0.8$
$8.6-9.4=-0.8$
$7.8-8.6=-0.8$
Step 3
As it follows the common difference procedure therefore it can be concluded that the given sequence is an arithmetic sequence and common difference ‘d’ is calculated to be as.
$d=10.2-11$
$=-0.8$

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