The sum of infinite terms of the following series $1+\dfrac {4}{5}+\dfrac {7}{{5}^{2}}+\dfrac {10}{{5}^{3}}+..$ will be

This is an arithmetico-geometric series where the sum is given by S = a/(1 - r) + dr/(1 - r)^2, with first term a = 1, common difference d = 3, and common ratio r = 1/5. Substituting these values gives S = 1/(4/5) + 3(1/5)/(4/5)^2, which simplifies to 5/4 + 15/16. Adding these fractions yields 35/16.

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