Question

The sum of how many terms oh an A.P. : 7,11,15,19,23,...will be 900?

Answer 1

here
a= 7
d=11-7=4
An=900
=>n/2{2a+(n-1)d} =900
=>n/2{2×7+(n-1)4} =900
=>n/2{14+4n-4}=900
=>n/2{10+4n}=900
=>10n+4n^2=2×900
=>4n^2+10n-1800=0
now solve the above given equation and definitely u will get the answer

Answer 2

Answer:

n’= -45/2 , n = 20

Step-by-step explanation:

Sn = n/2×[2a+(n-1)d] {a=7,d=4,Sn=900}

900=n/2×[2×7+(n-1)×4]

900=n/2×[14+4n-4]

900=n/2[14-4+4n]

900=n/2[10+4n]

900×2=n[10+4n]

1800=n[10+4n]

1800=[10n+4n²]

4n²+10n-1800=0

2(2n²+5n-900)=0

2n²+5n-900=0/2

2n²+5n-900=0

(Note:by splitting the middle term, we get;)

2n²+40n-45n-900=0

2n(n-20)+45(n-20)=0

(2n+45) (n-20)=0

(2n+45=0)/ (n-20=0)

n=(-45/2) or n=20.