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Yogita Ingle 6 years, 4 months ago
Weighted Mean is an average computed by giving different weights to some of the individual values. If all the weights are equal, then the weighted mean is the same as the arithmetic mean.
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Yogita Ingle 6 years, 4 months ago
For the first AP, a =3, d = 4
Hence, any nth term would be given by 3+(n-1)4 = 4n-1
Also, since 407 is the last term, so, 407 = 4n-1 i.e. maximum value of n can be 102
For the second AP, a = 2, d = 7
Hence any mth term would be given by 2+(m-1)7 = 7m - 5
Also, since 709 is the last terms, so, 709 = 7m-5 i.e. maximum value of m can be 102
To find the terms common to both the APs, we can equate the nth term of first AP to the mth term of the second AP
4n -1 = 7m-5
4n = 7m-4
Now, since n is a whole number, so 7m-4 needs to be divisible by 4.
So, then, m can be equal to all multiples of 4 till 102 i.e. 4, 8, 12, 16, 20, 24, ......100
So, the number of terms common to the 2 APs would be 25. >
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