IIM Bangalore (UGAT) (QA) PYQs

Let $A = \{a_1, a_2, ..., a_i, ...\}$ be an arithmetic progression, and let $B = \{b_1, b_2, ..., b_i, ...\}$ be a geometric progression.

The common difference for A is 2.

The common ratio for B is 0.2, and $b_1 = 0.8$

The infinite sum of the products $a_i b_i$ is 1, where $i = 1, 2, 3, ...$

What is $a_i$?