Write an explicit formula for the sequence. Use this, to find the 80th term of the sequence that begins: -3,1,5,9

see explanation

Step-by-step explanation:

There is a common difference d between consecutive terms in the sequence, that is

9 - 5 = 5 - 1 = 1 - (- 3) = 4

This indicates the sequence is arithmetic with n th term

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3 and d = 4, thus

= - 3 + 4(n - 1) = - 3 + 4n - 4 = 4n - 7 ← explicit formula

Thus

= 4(80) - 7 = 320 - 7 = 313

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3