Question

Consider the following arithmetic sequence. 3, \frac{11}{2} , 8,

(a) Identify d and {a}^1 .

d =

{a}^1 =

(b) Write the next three terms.

{a}^4 =

{a}^5 =

{a}^6 =

Answer 1

Answer: (a) a = 3, and d=
`(5)/(2)`

(b)
`a_4=(21)/(2)\\\\a_5=13\\\\a_6=(31)/(2)`

Explanation:

Since we have given that

Arithmetic sequence be

`3,(11)/(2),8`

As we know that

a denotes the first term.

d denotes the common difference.

So,
`a^1=3\\\\d=a_2-a_1=(11)/(2)-3=(11-6)/(2)=(5)/(2)`

Hence, a = 3, and d=
`(5)/(2)`

`a_4=a+3d=3+3*(5)/(2)=3+(15)/(2)=(6+15)/(2)=(21)/(2)\\\\a_5=a+4d=3+4* (5)/(2)=3+(20)/(2)=3+10=13\\\\a_6=a+5d=3+5* (5)/(2)=3+(25)/(2)=(6+25)/(2)=(31)/(2)`

Hence, (b)

`a_4=(21)/(2)\\\\a_5=13\\\\a_6=(31)/(2)`