What is this^
a=2,d=8,Sn=90 find n & an
Answers
Yo!
Here's the answer!
Given: a=2,d=8,Sn=90
To find: n and an.
Okay,so we know that,
Sn= n/2{(2a+(n-1)d}
Hence by substituting the value we get,
90= n/2{2×2+(n-1)×8}
90= n/2 (4+8n-8)
90= n/2 (-4+8n)
90×2= -4n+8n² ....(shifting 2 to the other side)
180= -4n+8n²
8n²-4n-180=0 .... (this is now in the form of a quadratic equation)
2n²-n-45=0 ..... (dividing the whole by 4.)
2n²-10n+9n-45=0 ...(by factorising,45×2 is 90,so 2 numbers are required so that when multiplied,they should be equal to the extreme left and right corners and also equal to the middle term.)
2n(n-5) +9(n-5) =O
(2n+9) (n-5) =0
n= -9/2 ain't possible,so
n=5.
So the value of n we found is 5,no substituting this value in this formula:
TN= a+(n-1)d ...(we only need to find TN now.)
tn= 2+(5-1)×8.
tn= 2+4×8
tn= 34.
Hope it helps!
–TGA. :)