Yesterday i was doing the question of arithmetic progressions of class 10th math of exercise 5.2. How i solve this question in easy way Find the number of terms in each of the following A.P. (i) 7, 13, 19, …, 205
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Find the number of terms in each of the following A.P. (i) 7, 13, 19, …, 205 Q.5(1)
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Therefore
First term, a = 7
Common difference, d = a2 − a1 = 13 − 7 = 6
Let there are n terms in this A.P.
an = 205
As we know, for an A.P.,
an = a + (n − 1) d
Therefore, 205 = 7 + (n − 1) 6
198 = (n − 1) 6
33 = (n − 1)
n = 34
Therefore, this given series has 34 terms in it.