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Sequences and Series question

2024 · 6 Apr · Shift 1 · Q56

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JEE Main
Mathematics
Sequences and Series
2024 · 6 Apr · Shift 1 · Q56

Sequences and Series question

2024 · 6 Apr · Shift 1 · Q56

JEE MainMathematicsSequences and SeriesNumerical+4 / −1

Let the first term of a series be

T_1=6

and its

r^{\text {th }}

term

T_r=3 T_{r-1}+6^r, r=2,3

, ............

n

. If the sum of the first

n

terms of this series is

\frac{1}{5}\left(n^2-12 n+39\right)\left(4 \cdot 6^n-5 \cdot 3^n+1\right)

, then

n

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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