Question

a1 = 5; a4 = 9 1/2; find a2, a3

Answer 1

GIVEN :

The values $a_1=5$ , $a_4=9\frac{1}{2}$

TO FIND :

The values of $a_2$ and $a_3$

SOLUTION :

Given that the first term and fourth terms of the sequence is $a_1=5$ , $a_4=9\frac{1}{2}$.

The formula for the nth term of the Arithmetic Sequence is given by:

$a_n=a_1+(n-1)d$

To find the terms $a_2$ and $a_3$:

Put n=4 in the above formula,

$a_4=9\frac{1}{2}=5+(4-1)d$

$\frac{19}{2}=5+3d$

$3d=\frac{19}{2}-5$

$3d=\frac{19-10}{2}$

$3d=\frac{9}{2}$

$d=\frac{9}{2}\times \frac{1}{3}$

$d=\frac{3}{2}$

∴ the common difference d is $\frac{3}{2}$

Put n=2 , $a_1=5$ and $d=\frac{3}{2}$ in the formula $a_n=a_1+(n-1)d$,

$a_2=5+(2-1)(\frac{3}{2})$

$a_2=5+1(\frac{3}{2})$

$a_2=\frac{10+3}{2}$

∴ $a_2=\frac{13}{2}$

Put n=3 , $a_1=5$ and $d=\frac{3}{2}$ in the formula $a_n=a_1+(n-1)d$,

$a_3=5+(3-1)(\frac{3}{2})$

$a_3=5+2(\frac{3}{2})$

$a_3=5+3$

∴ $a_3=8$

∴ The values are $a_2=\frac{13}{2}$ and $a_3=8$.

Answer 2

Answer:

a1 =5 a4 =9 1/2

a1 =a=5 ...........(1)

a4

=a+3d=5+3d=9

2

1

.......(2)

Equation (1)-(2), gives

−3d=5−

2

19

=

2

10−19

=

2

−9

⇒d=

2

3

∴a

2

=a+d=5+

2

3

=

2

13

∴a

3

=a+2d=5+2×

2

3

=8

∴a

2

=

2

13

,a

3

=8