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How do you find an equation that describes the sequence #4, 8, 12, 16,...# and find the 13th term?

Answer 1

Elijah Allen

#T_13 =52#

This sequence is an arithmetic progression because #T_2-T_1 =T_3-T_2=T_4-T_3=d=4#, where d = common difference.

For arithmetic progression, #T_n = a + (n-1)d#, where #a=#first term, n = number of term.

Therefore, #T_13 = 4 + (13-1)*4#

#T_13 = 4 + (12)*4#

#T_13 = 4 + 48 =52#

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Answer 2

Liam Brennan

The sequence is an arithmetic sequence with a common difference of 4. Therefore, the general equation for the nth term of the sequence is:

[ a_n = a_1 + (n - 1) \times d ]

Where: ( a_n ) = nth term of the sequence ( a_1 ) = first term of the sequence ( d ) = common difference between the terms ( n ) = position of the term in the sequence

Substituting the given values: ( a_1 = 4 ) ( d = 4 )

We can find the 13th term by plugging in ( n = 13 ) into the equation:

[ a_{13} = 4 + (13 - 1) \times 4 ]

[ a_{13} = 4 + 12 \times 4 ]

[ a_{13} = 4 + 48 ]

[ a_{13} = 52 ]

Therefore, the 13th term of the sequence is 52.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.