Check whether the given formula $a_{n} = n (n + 5)$ satisfies arithmetic sequence.

Not an arithmetic sequence

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An arithmetic sequence

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Finite series

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Solution

The correct option is B Not an arithmetic sequence
Assume $n = 1, 2, 3, . . . . . . .$
Put those values in $a_{n} = n (+ 5)$
$a_{1} = 1 (1 + 5) = 6$
$a_{2} = 2 (2 + 5) = 14$
$a_{3} = 3 (3 + 5) = 24$
$a_{4} = 4 (4 + 5) = 36$ .......
Therefore, the common difference, $d$ is not same.
So, it is not an arithmetic sequence.

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Check whether the given formula an=n(n+5) satisfies arithmetic sequence.

The correct option is B Not an arithmetic sequenceAssume n=1,2,3,.......Put those values in an=n(+5)a1=1(1+5)=6a2=2(2+5)=14a3=3(3+5)=24a4=4(4+5)=36 .......Therefore, the common difference, d is not same.So, it is not an arithmetic sequence.

Check whether the given formula $a_{n} = n (n + 5)$ satisfies arithmetic sequence.