If the first,second and last terms of an A.P. | vedclass

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(C) Given the first term $A = a$ and the second term $A + d = b$.Common difference $d = b - a$.The last term $l = 2a$. The formula for the last term i

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$\frac{3ab}{2(b - a)}$

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(C) Given the first term $A = a$ and the second term $A + d = b$.Common difference $d = b - a$.The last term $l = 2a$. The formula for the last term is $l = A + (n - 1)d$.Substituting the values: $2a = a + (n - 1)(b - a)$.$a = (n - 1)(b - a) \implies n - 1 = \frac{a}{b - a} \implies n = \frac{a}{b - a} + 1 = \frac{a + b - a}{b - a} = \frac{b}{b - a}$.The sum of an $A.P.$ is $S_n = \frac{n}{2}(A + l)$.$S_n = \frac{b}{2(b - a)}(a + 2a) = \frac{b}{2(b - a)}(3a) = \frac{3ab}{2(b - a)}$.

If the first,second and last terms of an $A.P.$ are $a, b$ and $2a$ respectively,then its sum is:

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