Question

How to find n and a with an=4 and d=2 and sn=-14 in arithmetic progression

Answer 1

Hey friend, here is your answer

Given=>
An=4
D=2
Sn= - 14
A= ?
N=?

=> an= a+ ( n-1) d

=> 4 = a + (n-1) 2

=> 4= a+2n-2

=> 4+2=a+2n

=> 6=a+2n

=> 6-2n=a __________(¡)




=> Sn=n/2{2a+(n-1)d}

=> -14= n/2 {2a+(n-1)d}

=> -14×2=n{2×(6-2n)+(n-1)2}

=>-28=12n-4n²+ 2n²-2n

=>-28=10n-2n²

=>2n²-10n-28=0

=>2n²-14n+4n-28=0

=>2n(n-7)+4(n-7)=0

=>(n-7) (2n+4)

=>n=7,-2




we will take n as 7


n=7

a=6-2n

a=6-14

a= -8

✌️ I HOPE IT HELPS. PLEASE MARK AS BRAINLIEST✌️