Question

a=2,d=8,Sn=90,find n and an

Answer 1

Answer:

38

AP=2,10,18,26,34.....

Step-by-step explanation:

Sn=n/2 [2a +[n-1]d]

90=n/2[4+[n-1]8]

90=n/2[4+8n-8]

90=n/2[-4+8n]

90=n[-2+4n]

90=-2n+4n2

4n2-2n-90=0

after solving this quadratic equation we get,

n=38

Answer 2

$\large{givenA=2,D=8,Sn=90}$

$\large{tofindNandAn}$

formula

$\large{Sn=n[2a+(n-1)d]/2}$

putting values we get

$\large{90=n[2(2)+(n-1)(8)/2}$

$\large{90=n[4+8n-8]2}$

$\large{180=n[-4+8n]}$

$\large{180=-4n+8nsq}$

then it become a quadratic equation...

$\large{8nsq-4n-180=0}$

using quadratic formula.....

-b+_√bsq-4ac/2a

values

b=-4

a=8

c=-180

then

$\large{4+_√(-4)sq-4(8)(-180)/2(8)}$

$\large{4+_√16+5760/16}$

$\large{4+_√5776/16}$

$\large{4+_76/16}$

two zeroes

$\large{4+76/16}$

$\large{4-76/16}$

$\large{80/16}$

$\large{-72/16}$

$\large{n=5}$

cause the value of n cannot be negative

then

$\large{theAnthterm}$

$\large{An=a+(n-1)d}$

$\large{An=2+(n-1)8}$

$\large{An=2+8n-8}$

$\large{An=8n-6}$