For a natural number n, let α n = 19ⁿ - 12ⁿ. Then, the value of (31α ₉ - α ₁₀)/(57α ₈) is _ _ _ _ _ _.

Sequence and Series: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Morning shift · Q49

JEE Main 202225 Jun, Morning shiftMathematicsMediumSequence and Series179× since 2002

For a natural number n, let

{\alpha _n} = {19^n} - {12^n}

. Then, the value of

{{31{\alpha _9} - {\alpha _{10}}} \over {57{\alpha _8}}}

is ___________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2022 · 25 Jun, Morning shift · Q49

JEE Main 202225 Jun, Morning shiftMathematicsMediumSequence and Series179× since 2002

For a natural number n, let

{\alpha _n} = {19^n} - {12^n}

. Then, the value of

{{31{\alpha _9} - {\alpha _{10}}} \over {57{\alpha _8}}}

is ___________.

Your answerType your answer. Integers and decimals are accepted.