Question

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

Answer 1

Answer:  (a) a = 3, and d=$\dfrac{5}{2}$

(b) $a_4=\dfrac{21}{2}\\\\a_5=13\\\\a_6=\dfrac{31}{2}$

Step-by-step explanation:

Since we have given that

Arithmetic sequence be

$3,\dfrac{11}{2},8$

As we know that

a denotes the first term.

d denotes the common difference.

So, $a^1=3\\\\d=a_2-a_1=\dfrac{11}{2}-3=\dfrac{11-6}{2}=\dfrac{5}{2}$

Hence, a = 3, and d=$\dfrac{5}{2}$

$a_4=a+3d=3+3\times\dfrac{5}{2}=3+\dfrac{15}{2}=\dfrac{6+15}{2}=\dfrac{21}{2}\\\\a_5=a+4d=3+4\times \dfrac{5}{2}=3+\dfrac{20}{2}=3+10=13\\\\a_6=a+5d=3+5\times \dfrac{5}{2}=3+\dfrac{25}{2}=\dfrac{6+25}{2}=\dfrac{31}{2}$

Hence, (b)

$a_4=\dfrac{21}{2}\\\\a_5=13\\\\a_6=\dfrac{31}{2}$