If
find the value of $t_n=S_n-S_{n-1}$"

Given: Sn =  $4n^{2} + 5n +8$

To find: We have to find  $t_n = S_n - S_{n-1}$.

Solution:

$t_3 = 4(3)^{2} + 5(3) + 8 - (4(2)^{2} + 5(2) + 8)$

          = $36 +15 + 8 - 16 -10 - 8 = 25$

$t_5 =4(5)^{2} + 5(5) + 8 - (4(4)^{2} + 5(4) + 8)$

    = $100 +25 + 8 - 64 -20 - 8 = 41$

$t_7 = 4(7)^{2} + 5(7) + 8 - (4(6)^{2} + 5(6) + 8)$

      = $196 +35 + 8 - 144 -30 - 8 = 57$

So, $t3 +  t5 + t7 = 25 + 41 + 57 = 123$

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Updated on: 10-Oct-2022

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