If an= 4; d = 2 And Sn = -24; Find n
Answers
sn=n/2[a+(n-1)d]
-24=n/2[4+(n-1)2]
-24=n/2[4+2n-2]
-24=n/2(2+2n)
-24=n+n²
n²+n+24=0
solve the equation and get the value of n
Answer:
Answer
(i)
Here a=2,d=8,S
n
=90
We know S
n
=
2
n
[2a+(n−1)d]
90=
2
n
[2⋅2+(n−1)8]
⇒180=n[4+8n−8]
⇒180=8n
2
−4n
⇒8n
2
−4n−180=0
⇒2n
2
−n−45=0
⇒(n−5)(2n+9)=0
⇒n=5,−
2
9
⇒n=5 (since n cannot be negative)
Therefore a
n
=a+4d=2+4(8)=2+32=34
(ii)
Here d=5,S
9
=75
We know S
n
=
2
n
[2a+(n−1)d]
S
9
=
2
9
[2a+(8)d]
⇒75=
2
9
[2a+8(5)]
⇒75=
2
9
[2a+40]
⇒75=9[a+20]
⇒75=9a+180
⇒9a=−105
⇒a=−
3
35
Therefore a
9
=a+8d=−
3
35
+8(5)=
3
85
(iii)
Here a=7,a
13
=35
We know a
n
=a+(n−1)d
⇒a
13
=7+(13−1)d
⇒35=7+12d
⇒28=12d
⇒d=
3
7
We know S
n
=
2
n
[2a+(n−1)d]
S
13
=
2
13
[2(7)+(13−1)
3
7
]
=
2
13
[14+12×
3
7
]
=
2
13
[14+28]
=
2
13
(42)
=13×21
S
13
=273