Question

if s4=16 and s5=12 then find the value of an​

Answer 1

GIVEN :

If $s_4=16$ and $s_5=12$ then find the value of $a_n$

TO FIND :

The ​value of $a_n$

SOLUTION :

Given that $s_4=16$ and $s_5=12$

We know the formula $s_n=a+(n-1)d$

Put n=4 in $s_4=16=a+(4-1)d$

$a+3d=16\hfill (1)$

Put n=5 in $s_5=12=a+(5-1)d$

$a+4d=12\hfill (2)$

Subtracting the equations (1) and (2) we get

a+3d=16

a+4d=12  (-)

_________

-d = 4

d=-4

Substitute the value d=-4 in equation (1)

a+3(-4)=16

a-12=16

a=16+12

a=28

The formula for nth term is $a_n=a+(n-1)d$

$a_n=28+(n-1)(-4)$

=28-4n+4

=32-4n or =4(8-n)

$a_n=32-4n$

The value of $a_n$ is 32-4n

Answer 2

Step-by-step explanation:

${S}^{5} = 35$

$= > \frac{n}{2} [2a + (n - 1)d] = 35$

$= > \frac{5}{2} [2a + 4d] = 35$

$= > 2a + 4d = 35 \times \frac{2}{5}$

$= > 2a + 4d = 7 \times 2$

$= > 2a + 4d = 14 \: \: \: \: \: \: \: \: \: \: --------1$

${S}^{4} = 22$

$= > \frac{4}{2} [2a + (4 - 1)d] = 22$

$= > 2[2a + 3d] = 22$

$= > 2a + 3d = 11 \: \: \: \: \: \: \: \: \: \: -------- \: 2$

On subtracting equation 1 and 2, we get

d = 3

Now

On substituting the value of d in equation 1, we get

$= > 2a + 4 \times 3 = 14$

$= > 2a + 12 = 14$

$= > 2a = 2$

$= > a = 1$

$5th\:term = a + 4d$

$= 3 + 4 \times 2$

$= 3 + 8$

$= 11$