Question

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Answer 1

The first 5 terms in an arithmetic sequence is 4,2,0,-2,-4

Explanation:

The general form of an arithmetic sequence is

$a(n)=a+(n-1)d$

where a denotes the first term of the sequence, d denotes the common difference.

Here a = 4 and d = -2

To determine the consecutive terms of the sequence, let us substitute the values for n.

To find the second term, substitute n = 2 in the formula $a(n)=a+(n-1)d$

$a(2)=4+(2-1)(-2)$

Simplifying,

$a(2)=4-2=2$

Similarly,

For n = 3,

$a(3)=4+(2)(-2)=0$

For n = 4,

$a(4)=4+(4-1)(-2)\\a(4)=4+(3)(-2)\\a(4)=4-6\\a(4)=-2$

For n = 5,

$a(5)=4+(5-1)(-2)\\a(5)=4+(4)(-2)\\a(5)=4-8\\a(5)=-4$

Thus, the first 5 terms of the arithmetic sequence is 4,2,0,-2,-4