Q. 65.0( 1 Vote )

How many terms are there in the following Arithmetic Progressions?

(i) (ii) 7, 13, 19, …, 205.

Answer :

(i) Here, first term, a = -1


Last term, l =


We know that common difference, d = a1 – a.


d = – (-1) = + 1 = =


We know that Number of terms, n = () + 1.


n = + 1


= + 1


= + 1


= (13 × 2) + 1


= 26 + 1


= 27


There are 27 terms in the given A.P.


(ii) Here, first term, a = 7


Last term, l = 205


We know that common difference, d = a1 – a.


d = 13 - 7 = 6


We know that Number of terms, n = () + 1.


n = + 1


= + 1


= 33 + 1


= 34


There are 34 terms in the given A.P.


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