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

Mar 21, 2016

Use the formula ${s}_{n} = \frac{n}{2} \left(2 a + \left(n - 1\right) d\right)$

Explanation:

a is the first term.

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

$781 = 11 \left(2 a + 63\right)$

$781 = 22 a + 693$

$88 = 22 a$

$4 = a$

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.