How many terms are identical in APs 1,3,5,.... upto 120 terms and 3,6,9,.... upto 80 terms?????

AP1 : 1, 3, 5, ...

 

In this AP, a = 1 and d = 2

 

T₁₂₀ = a + (120-1)d = 1 + 119*2 = 239

 

So this AP contains all the odd numbers from 1 till 239.

 

 

AP2 : 3, 6, 9, ...

 

In this AP, a = 3 and d = 3

 

T₈₀ = a + (80-1)d = 3 + 79*3 = 240

 

So this AP contains all the multiples of 3 from 3 till 240.

 

 

Since every second multiple of 3 (starting from 3) is an odd number, hence every second term of the AP2 (starting from first term) is also in AP1.

 

So total number of terms in AP2 which are in AP1 as well are 80/2 = 40.