Question

how many terms of the ap 9,6,3,.....will be needed to give the sum -216.

Answer 1

a=9
d=6-9=-3
Sn=-216
Sn=n/2[2a+(n-1)d]
=>-216=n/2[2*9+(n-1)(-3)]
=>-216=n/2(18-3n+3)
=>-216 *2=n(21-3n)
=>-432=21n-3n ²
=>3n²-21n-432=0
=>3(n²-7n-144)=0
=>n²-7n-144=0
=>n²-(16-9)n-144=0
=>n²-16n+9n-144=0
=>n(n-16)+9(n-16)=0
=>(n+9) (n-16)=0
=>n+9=0 or n-16=0
=>n=-9 or n =16
Since a term cannot be negative.Therefore - 9 is rejected. Therefore 16 terms of the given ap can give the sum - 216.
I think it will help you dear.

Answer 2

Answer:

there are 16 terms of the given ap

Step-by-step explanation:

n=? Sn= 216 ,a=9

d=6-9=-3

d=-3

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

-216=n/2(18-3n+3)

-216= n/2(21-3n)

-216×2=21n-3n square

(÷3 the whole equation )

n square -7n-144=0

n(n-16)+9(n-16)=0

(n-16) (n+9)=0

where n=16 or -9

hence -9 is agreed.

There are 16 terms needed to give a sum of -216

hope the answer helped you all thank you so much be kind with all.

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