Let $$a1$$,$$a2$$,$$a3$$,$$a4$$ and $$a5$$ be such that $$a1$$,$$a2$$ and $$a3$$ are in A.P ,$$a2$$,$$a3$$ and $$a4$$ are in G.P.; and $$a3$$,$$a4$$ and $$a5$$ are in H.P. Then $$a1$$,$$a3$$ and $$a5$$ are in

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Let $$a1$$,$$a2$$,$$a3$$,$$a4$$ and $$a5$$ be such that $$a1$$,$$a2$$ and $$a3$$ are in A.P ,$$a2$$,$$a3$$ and $$a4$$ are in G.P.; and $$a3$$,$$a4$$ and $$a5$$ are in H.P. Then $$a1$$,$$a3$$ and $$a5$$ are in

Infinity Learn · Accepted Answer

We have, $$a1$$,$$a2$$,$$a3are$$ in A.P.⇒$$2a2=a1+a3----i$$ $$a2$$,$$a3$$,$$a4are$$ in G.P.⇒$$a32=a2a4-----ii$$ $$a3$$,$$a4$$,$$a5are$$ in H.P.⇒$$a4=2a3a5a3+a5-----iiiPutting$$ $$a2=a1+a32$$ and $$a4=2a3a5a3+a5$$ in (ii), we $$geta32=a1+a32$$×$$2a3a5a3+a5$$⇒ $$a32=a1a5$$⇒$$a1$$,$$a3$$,$$a5are$$ in G.P.

Let $a_{1}, a_{2}, a_{3}, a_{4} and a_{5}$ be such that $a_{1}, a_{2} and a_{3}$ are in A.P , $a_{2}, a_{3} and a_{4}$ are in G.P.; and $a_{3}, a_{4} and a_{5}$ are in H.P. Then $a_{1}, a_{3} and a_{5}$ are in

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Let a1,a2,a3,a4 and a5 be such that a1,a2 and a3 are in A.P ,a2,a3 and a4 are in G.P.; and a3,a4 and a5 are in H.P. Then a1,a3 and a5 are in

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Let $a_{1}, a_{2}, a_{3}, a_{4} and a_{5}$ be such that $a_{1}, a_{2} and a_{3}$ are in A.P , $a_{2}, a_{3} and a_{4}$ are in G.P.; and $a_{3}, a_{4} and a_{5}$ are in H.P. Then $a_{1}, a_{3} and a_{5}$ are in