    Question

# Find the number of terms in each of the following APs respectively: (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=13−7=19−13=6 an=205 Using formula an=a+(n−1)d to find nth term of arithmetic progression, we get ⇒an=a+(n−1)d ⇒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 ⇒an=a+(n−1)d ⇒−47=18+(n−1)(−52) ⇒−47=18−5n2+52 Multiplying by 2 on both sides, we get, ⇒−94=36−5n+5 ⇒5n=94+36+5=135 ⇒n=1355=27 Therefore, there are 27 terms in the given arithmetic progression.  Suggest Corrections  0      Similar questions  Related Videos   General Term of an AP
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