Using $V_{n}$ method, if $T_{n}$ = (3n - 1)(3n + 2), Find the value of K if $V_{n}$ - $V_{n - 1}$ = K $T_{n}$ __

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Solution

$T_{n}$ = (3n - 1)(3n + 2)

Let $V_{n}$ = (3n - 1)(3n + 2)(3n + 5)

$V_{n - 1}$ = (3n - 4)(3n - 1)(3n + 2)

$V_{n}$ - $V_{n - 1}$ = (3n - 1)(3n + 2) [3n + 5 - (3n + 4)]

= 9.(3n - 1)(3n + 2)

= 9. $T_{n}$

$∴$ K = 9

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