If (1+3+5+..... upto n terms)/(2+5+8+....... upto 8 terms) = 25, then find the value of n
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Answer:
AP
Ist
→2,5,8,.......50
th
term⇒a=2,d=3,
AP
2nd
→3,5,7,9,.....60
th
term⇒a=3,d=2
ForgeneraltermI
st
A.P.⇒
a
n
1
=2+(n
1
−1)3
a
n
1
=3n
1
−1
Forgeneralterm2
nd
A.P⇒
a
n
2
=3+(n
2
−1)2
a
n
2
=2n
2
+1
Ifa
n
1
=a
n
2
3n
1
−1=2n
2
+1⇒3n
1
−2n
2
=2
⇒3n
1
=2+2n
2
⇒3n
1
=2(n
2
+1)⇒[
2
n
1
+
3
n
2
+1
=k]
2
n
1
=k
n
1
=2k
n
1
≤50
2k≤50
k≤25
k≤20Sopossiblevalueofk=1,2,3,.....20
3
n
2
+1
=k
n
2
=3k−1
n
2
≤60
3k≤61
k≤
2
61
≈20.3....
[Givenabove]
There are 20 identical terms in A.P.
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