Find 3.7+5.10+7.13+9.16+......+ n terms

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Solution

$3.7 + 5.10 + 7.13 + - - n l e m n s$

$G e n e r a l t e r m 4_{2} = Pr 9 r$

$G e n e r a l t e r m o f 3, 5, 7, -; 2 η + 1$

$Pr = 2 η + 1$

$G e n e r a l t e r m o f 7, 10, 13,$

$3 η + 4$

$q r = 3 η + 4$

$Y r = (2 n + 1) (3 n + 4)$

$S n = n \sum r = 1 4 r$

$n \sum r = 1 (6 n^{2} + 11 n + 4)$

$6 \sum n^{2} + 11 \sum n + 4 \sum 1$

$6. \frac{n (n + 1) (2 n + 1)}{6} + 11 \frac{n (n + 1)}{2} + 4 n$

$n (n + 1) (2 n + 1) + \frac{11 n (n + 1)}{2} + 4 n$

$\frac{n (n + 1)}{2} [4 n + 2 + 11 n^{2} + 11 n + 8 n]$

$\frac{n (n + 1)}{2} (11 n^{2} + 23 n + 2)$

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