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Question

Find $$a , b$$ such that $$7.2 , a , b , 3$$ are in AP.


Solution

Given $$7.2,a,b,3$$ are in $$A.P$$
$$\implies 7.2,a,b$$ are in $$A.P$$
$$\implies 2{a}=7.2+b\implies b=2{a}-7.2$$
and also $$ a,b,3$$ are in $$A.P$$
$$\implies 2{b}=a+3\implies 2(2{a}-7.2)=a+3$$
$$\implies 4{a}-14.4=a+3$$
$$\implies 3 a=17.4\implies a=5.8$$
$$b=2(5.8)-7.2=11.6-7.2=4.4$$

Mathematics

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