2) Given the sequence 5, -2, -9, ... Find the first term:

Is the sequence arithmetic?

Find the common difference d:

Find the general term an:

Find the 20th term:

Find the sum of the first 50 terms:

Find the first term:  

The first term is 5

Is the sequence arithmetic?

Yes because (5 -7 = -2) (-2 - 7 = -9)  

Find the common difference d:

The common difference is -7

Find the general term an:

= (first term) + ((nth term) -1) · (common difference)

= 5 + (n - 1) · (-7)

Find the 20th term:

= 5 + (20 - 1) · (-7)

= -128

Find the sum of the first 50 terms:

= 5 + (50 - 1) · (-7)

= -338

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116