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Question

Find the number of terms in each of the following APs:

(i) 7,13,19....,205

(ii) 18,312,13,...47


A

34, 27

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B

26, 35

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C

27, 34

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D

35, 26

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Solution

The correct option is A

34, 27


(i) 7,13,19....,205

First term, a=7

Common difference, d=137=6

an=205

Using formula an=a+(n1)d to find nth term of arithmetic progression, we get

205=7+(n1)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=31218=52

an = − 47

Using formula an=a+(n1)d to find nth term of arithmetic progression, we get

47=18+(n1)(52)

94=365n+5

5n=135
n=1355=27

Therefore, there are 27 terms in the given arithmetic progression.


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