This is the Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.
Here the AP and the last term of AP is given you have to find the number of terms in the given AP.
This is the Question Number 7 Exercise 11 A of RS Aggarwal Solution.
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How many terms are there in the AP 6, 10, 14, 18, …. 174?
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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.