Question

Determine the first five terms of the sequence defined by the following explicit formula:

an= -4n-5
show steps please

Answer 1

To find:-

• The first 5 terms of the sequence using the given explicit formula.

Answer:-

The given explicit formula to us is ,

`\implies a_n = -4n - 5 \\`

For finding 1st term put n = 1 in the given formula as ,

`\implies a_1 = -4(1) - 5 \\`

`\implies a_1 = -4 - 5 =\boxed{-9} \\`

Likewise put n = 2 to find out the second term ,

`\implies a_2 = -4(2) - 5 \\`

`\implies a_2 = -8-5 =\boxed{-13}\\`

Similarly , we can find third, fourth and fifth term as ,

`\implies a_3 = -4(3) - 5 \\`

`\implies a_3 = -12 - 5 =\boxed{-17} \\`

`\implies a_4 = -4(4) -5 \\`

`\implies a_4 = -16 -5 =\boxed{-21} \\`

`\implies a_5 = -4(5) -5\\`

`\implies a_5 = -20-5=\boxed{-25} \\`

Hence the first 5 terms of the sequence are -9 , -13 , -17 , -21 and -25 .

and we are done!

Answer 2

-9, -13, -17, -21, -25

Explanation:

The explicit formula for the sequence is given by an = -4n - 5. To find the first five terms of the sequence, we can simply substitute the values of n from 1 to 5 in the formula and calculate the corresponding values of a(n).

a1 = -4(1) - 5 = -9

a2 = -4(2) - 5 = -13

a3 = -4(3) - 5 = -17

a4 = -4(4) - 5 = -21

a5 = -4(5) - 5 = -25

Therefore, the first five terms of the sequence are:

-9, -13, -17, -21, -25