The number of common terms in the progressions 4 , 9 , 14 , 19 , … … , up to 25 th term and 3 , 6 , 9 , 12 ,.... up to 37 th term is :

Step-by-step solution

4 , 9 , 14 , 19 , … , up to 25 th term ⇒ T 25 = 4 + ( 25 - 1 ) 5 ⇒ T 25 = 4 + 120 ⇒ T 25 = 124 3 , 6 , 9 , 12 , … , up to 37 th term ⇒ T 37 = 3 + ( 37 - 1 ) 3 ⇒ T 37 = 3 + 108 ⇒ T 37 = 111 Common difference of I st series is d 1 = 5 Common difference of II nd series is d 2 = 3 First common term = 9 , and their common difference = 15 ( LCM of d 1 and d 2 . So, the common terms are 9 , 24 , 39 , 54 , 69 , 84 , 99 .