Question

How many term are there in the A.P.?
(i)7,10,13,...43.
(ii)-1,$-\frac{5}{6},-\frac{2}{3},-\frac{1}{2},...,\frac{10}{3}$
(iii) 7,13,19,...,205.
(iv)18,$15\frac{1}{2}$,13,...,-47.

Answer 1

1-
T=a+(n-1)d
43= 7+(n-1)3
36/3= n-1
n = 12+1=13
2-
T=a+(n-1)d
10/3= -1+(n-1)1/6
26= n-1
n = 27
3-
T=a+(n-1)d
205= 7+(n-1)6
198/6= n-1
n = 33+1=34
4-
T=a+(n-1)d
-47= 18+(n-1)(-5/2)
(-65 x 2)/(-5)=n-1
n-1=26
n=27