How do you find the first term of the arithmetic sequence having the data given $S_{n} = 781$ $S_n= 781$ , d = 3, n = 22?

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Answer 1 · 2016-03-21T20:56:25

Use the formula $s_{n} = \frac{n}{2} (2 a + (n - 1) d)$ $s_n = n/2(2a + (n - 1)d)$

a is the first term.

$781 = \frac{22}{2} (2 a + (22 - 1) 3)$ $781 = 22/2(2a + (22 - 1)3)$

$781 = 11 (2 a + 63)$ $781 = 11(2a + 63)$

$781 = 22 a + 693$ $781 = 22a + 693$

$88 = 22 a$ $88 = 22a$

$4 = a$ $4 = a$

Practice exercises:

An arithetic sequence of 14 terms has a sum of -322. The first term is -2. Find the common ratio, r.

Good luck.

How do you find the first term of the arithmetic sequence having the data given Sn=781S_n= 781, d = 3, n = 22?