Question

In an AP
given a = 2, d=8, S = 90, find n
​

Answer 1

hi there mate!!!

Solution:

Here,

a=2,

d=+8

S=90

by the formula,

S=n/2[2a+(n-1)×d]

90= n/2[2×2+(n-1)×8]

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

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

90=n/2×-4+8n

90=-4n+8n^2/2

90×2=-4n+8n^2

180=-4n+8n^2

now,

8n^2-4n-180=0.....(required quadratic polynomial)

dividing by 4,

2n^2-n-45=0

by factorization method,

2n^2-10n+9n-45=0

2n(n-5) +9(n-5) =0

hence,

(n-5) (2n+9) =0

n=5 or n= -9/2

we know,

number of terms can never be negative,

so, n=- 9/2 is discarded.

hence,

n= 5

therefore the number of terms is 5

Checking:

here,

first term= 2, and difference= 8 and sum= 90

hence,

first term= 2

second term= 2+8= 10

third term= 10+8=18

fourth term=18+8=26

fifth term= 26+8=34

sum= addition of all terms

90= 2+10+18+26+34

90=90

hence,there are 5 terms

hope this helps! ☺♥✌