Using a formula determine what term in the arithmetic sequen

Using a formula, determine what term in the arithmetic sequence: 2, 6, 10, 14, .... is the number 406? Using a formula, find a_1 when d = 4 and a_8 = 33 in an arithmetic sequence.

Solution

3) S = 2, 6 , 10 , 14

nth term : an = a1 + (n-1)d

d = 4

406 = 2 +4(n-1)

4n -4 = 404

4n = 408 ----> n = 102

4) a8 = 33 , d = 4 , find a1

an = a1 + (n-1)d

a8 = a1 + (8-1)*4

33 = a1 + 28

a1 = 5