Find the number of terms in each of the following APs:
(i) 7,13,19....,205
(ii) 18,312,13,...−47
34, 27
(i) 7,13,19....,205
First term, a=7
Common difference, d=13−7=6
an=205
Using formula an=a+(n−1)d to find nth term of arithmetic progression, we get
205=7+(n−1)6
⇒205=6n+1
⇒204=6n
⇒n=2046=34
Therefore, there are 34 terms in the given arithmetic progression.
(ii) 18,312,13,...−47
First term, a=18
Common difference, d=312−18=−52
an = − 47
Using formula an=a+(n−1)d to find nth term of arithmetic progression, we get
−47=18+(n−1)(−52)
⇒−94=36−5n+5
⇒5n=135
⇒n=1355=27
Therefore, there are 27 terms in the given arithmetic progression.