Let S be the sum of the first 9 terms of the series: x + k a + x² + (k + 2) a + x³ + (k + 4) a + x⁴ + (k + 6) a +.... where a ≠ 0 and x ≠ 1. If S = (x¹⁰ - x + 45a(x - 1))/(x - 1), then k is equal to:

Sequence and Series: JEE Main 2020 Mathematics question

JEE Main 2020 · 2 Sep, Evening shift · Q5314

JEE Main 20202 Sep, Evening shiftMathematicsMediumSequence and Series179× since 2002

Let S be the sum of the first 9 terms of the series : {x + k

a

} + {x² + (k + 2)

a

} + {x³ + (k + 4)

a

} + {x⁴ + (k + 6)

a

} + .... where a

\ne

0 and x

\ne

1. If S =

{{{x^{10}} - x + 45a\left( {x - 1} \right)} \over {x - 1}}

, then k is equal to :