help with fraction sequences please xox

The Term n :Tn of an arithmetic sequence can be given by

Tn = a + (n-1)d

where n is the nth term

a is the first term and d is the common difference ( ie any term less the previous term)

so T1 = a + (1-1)d=a

T2 = a +(2-1)d= a+d

T3 = a + (3-1)d = a+2d and so on

In your problem note that the numerator of any Tn is n

The denominator : first term is 3 ; common difference is 2 so denominator is Tn = a + (n-1)d = 3 +2(n-1)

numerator/denominator Tn = n/( 3 + 2(n-1))

*2 Substitution

Tn = n/ (n^2 +1)

then for T1 replace each n with 1 : 1/(1^2 +1 ) = 1/2

similarly for next 3 terms T2, T3 and T4