Find the 2nd term of an arithmetic sequence with t5 = 3 and t7 = 7?
The nth term of an arithmetic sequence is defined as:
`a_(n) = a + (n - 1)d`
d represents the common difference. Since the 5th term = 3 and the 7th term = 7, the common difference = 2.
In this case, to find the 2nd term, subtract 2, t4 = 1, t3 = -1, so t2 = -3
To use formula: find the first term a by substituting a term that is given to find a.
3 = a + (5-1)2 By substituting the 5th term = 3.
3 = a + 8
a = -5 Now use this to find 2nd term by plugging in to equation.
`a_(n) = -5 + (2 - 1)2`
`a_(n) = -5+2`
So the 2nd terms is -3.