If the first term of a G.P. a_1, a_2, a_3, do | vedclass

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(A) Let the first term $a_1 = 1$ and the common ratio be $r$.Then the terms are $a_1 = 1, a_2 = r, a_3 = r^2$.We want to minimize the expression $f(r)

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$-0.4$

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(A) Let the first term $a_1 = 1$ and the common ratio be $r$.Then the terms are $a_1 = 1, a_2 = r, a_3 = r^2$.We want to minimize the expression $f(r) = 4a_2 + 5a_3 = 4r + 5r^2$.To find the minimum,we take the derivative with respect to $r$ and set it to zero:$f'(r) = \frac{d}{dr}(4r + 5r^2) = 4 + 10r = 0$.Solving for $r$:$10r = -4 \Rightarrow r = -\frac{4}{10} = -0.4$.Since $f''(r) = 10 > 0$,the function has a minimum at $r = -0.4$.

If the first term of a $G.P.$ $a_1, a_2, a_3, \dots$ is unity such that $4a_2 + 5a_3$ is least,then the common ratio of the $G.P.$ is

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