Question
Find the number of terms in each of the following APs:
(i) 7,13,19....,205
(ii) 18,312,13,...−47
(i) 7,13,19....,205
(ii) 18,312,13,...−47
Answer: Option A
:
A
(i) 7,13,19....,205
First term, a=7
Common difference, d=13−7=6
an=205
Using formulaan=a+(n−1)d to findnthterm 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 formulaan=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.
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:
A
(i) 7,13,19....,205
First term, a=7
Common difference, d=13−7=6
an=205
Using formulaan=a+(n−1)d to findnthterm 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 formulaan=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.
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