Subjective Type

Find four terms which are in G.P., whose third term is $$4$$ more than first term and second term is $$36$$ more than $$4^{th}$$ term.

Solution

According to the question
Third term=first term+4
$$ar^2=a+4$$
$$a(r^2-1)=4$$
According to the question
Second term=fourth term$$+36$$
$$ar=ar^3+36$$
$$ar(1-r^2)=36$$
Divide equation (ii) by (i), we get
$$\dfrac{ar(1-r^2)}{a(r^2-1)}=\dfrac{36}{4}$$
$$-r=9$$
$$r=9$$
put $$r=-9$$ in eq (i)
$$a((-9)^2-1)=4$$
$$a(81-1)=4$$

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