We have given a series of AP 6, 10, 14, 18,….174 and we have to asked to find its number of terms in this AP?
Book – RS AGGARWAL,
class 10, Arithmetic Progression, chapter 5A, question no 7
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Given: AP is 6,10,14,18,......,174
Here, first term =a=6
Common difference =d=10−6=4
To find: the number of terms(n)
Last term=a+(n−1)d
174=6+(n−1)4
174−6=(n−1)4
n−1=168/4=42
n=42+1=43
There are 43 terms.