In an AP, if first term is one and sum of first 100 terms is 19900 then find the common difference
Answers
Answered by
0
Step-by-step explanation:
a
1
,a
2
,a
3
,....,a
99
,a
100
areinap
Leta
1
=a
commondifference,=d
a
2
=a+da
3
=a+2d
s
n
=
2
n
[2a
1
+(n−1)d]
s
100
=
2
100
[2a+99d]
=50[2a+99d]=−1−−−−(1)
eventermsa
2
,a
4
,...a
100
(n=50)
a
2
=a+d,a
4
=a+2d
commondifference=(a+3d)−(a+d)
S
e
=
2
50
[2(a+d)+49×2d]=1
25(2a+2d+98d)=1
25(2a+100d)=1−−−−(2)
Fromequation(1)and(2)weget
s=
50
3
anda=
50
−149
a
100
=a
1
+99d
=−
50
149
+99×
50
3
=
50
148
∴a
100
=
25
148
G.Pa=
25
47
,r=
50
3
s
∞
=
1−r
a
=
1−
50
3
25
47
=
25
47
×
47
50
=2.
Answered by
1
Step-by-step explanation:
n=100
a=1
Sn=19900
Sn=(n/2)*(a+an)
19900=(100/2)*(1+an)
19900=50*(1+an)
19900/50=1+an
396=1+an
an=395
an=a+(n-1)*d
395=1+(100-1)*d
395-1=99*d
394/99=d
d=3.97
Common difference is 3.97
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