QJEEM22Ma4754: JEE Main 2022 Mathematics - Class 11 JEEM22Ma4754 Solution: If a 1 , a 2 , a 3 ...... and b 1 , b 2 , b 3 ....... are A.P., …

a₁, a₂, a₃ .... are in A.P. (Let common difference is d₁)

b₁, b₂, b₃ .... are in A.P. (Let common difference is d₂)

and a₁ = 2, a₁₀ = 3, a₁b₁ = 1 = a₁₀b₁₀

$$\because$$ a₁b₁ = 1

$$\therefore$$ b₁ = $$\frac{1}{2}$$

a₁₀b₁₀ = 1

$$\therefore$$ b₁₀ = $$\frac{1}{3}$$

Now, a₁₀ = a₁ + 9d₁ $$\Rightarrow$$ d₁ = $$\frac{1}{9}$$

b₁₀ = b₁ + 9d₂ $$\Rightarrow$$ d₂ = $$\frac{1}{9}$$$$\left[\frac{1}{3}-\frac{1}{2}\right]$$ = $$-$$ $$\frac{1}{54}$$

Now, a₄ = 2 + $$\frac{3}{9}$$ = $$\frac{7}{3}$$

b₄ = $$\frac{1}{2}$$ $$-$$ $$\frac{3}{54}$$ = $$\frac{4}{9}$$

$$\therefore$$ a₄b₄ = $$\frac{28}{27}$$