7) if 3+5+7+............ to n terms = 5+8+11........... are in ap
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Explanation:
P=3+5+7+...(n terms)
a=3
d=5-3=2
∴P=2n[2.3+(n−1)2]=n2+2n
Q=5+8+11+...(10 terms)
a=5
d=8-5=3
∴Q=210[2.5+(10−1)3]=185
∴QP=7
⇒185n2+2n=7
⇒n2+2n−1295=0
⇒(n−35)(n+37)=0
∴n=35
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