Find-the-sum-of-the-series-2-5-8-12-n-

Question Number 10369 by Tawakalitu ayo mi last updated on 05/Feb/17

Find the sum of the series

2 + 5 + 8 + 12 \dots n

Commented by mrW1 last updated on 06/Feb/17

t h e n - t h t e r m o f t h e s e r i e s i s n o t

c l e a r . p l e a s e c h e c k .

Answered by arge last updated on 06/Feb/17

d = 3

a_{1} = 2

a_{n} = ?

a_{n} = a_{1} + (n - 1) d

a_{n} = 2 + 3 n - 3

a_{n} = 3 n - 1

a_{n} = \frac{2 S_{n}}{n} - a_{1}

3 n^{2} - n = 2 S_{n} - a_{1} n

3 n^{2} + n = 2 S_{n}

S_{n} = \frac{n (3 n + 1)}{2}

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