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

Asked by Palak Shrivastava | 11th Nov, 2013, 06:37: AM

Expert Answer:

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.

Answered by Rashmi Khot | 11th Nov, 2013, 09:55: AM

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