The first element in an arithmetic sequence is 2. Its twenty second is 14. Find the value of n so that a (n) = 6

n = 8

Step-by-step explanation:

Given the nth term of an arithmetic sequence to be Tn = a + (n-1) d

a = first term of the sequence

n = number of terms

d = common difference.

Given the first element a = 2 and 22nd to be 14

T22 = a + (22-1) d = 14

a+21d = 14

Substtuting a = 2 into the equation to get d

2+21d = 14

21d = 12

d = 12/21

d = 4/7

The nth term of the sequence given a = 2 and d = 4/7 will be expressed as;

Tn = 2 + (n-1) 4/7

Given Tn = 6

6 = 2 + (n-1) 4/7

6 = 2+4/7 n - 4/7

6-2+4/7 = 4/7 n

32/7=4/7 n

32 = 4n

n = 32/4

n = 8