Question

find the number of terms in the following series 1,7,13,19,_______,199

Answer 1

first term (a ) = 1
common difference (d) = 7 - 1 = 6
$T_n=199$
we know,
Tn = a + (n - 1)d
199 = 1 + (n - 1)6
199 -1 = 6(n-1)
198/6 = n -1
33 + 1 = n
n = 34

hence, number of terms = 34

Answer 2

a=1
d=a2-a1=7-1=6
an=a+(n-1)d
199=1+(n-1)6
199=1+6n-6
199=-5+6n
199+5=6n
204=6n
34=n