The sum of the common terms of the following three arithmetic progressions 3, 7, 11, 15, ...., 399; 2, 5, 8, 11, ...., 359 and 2, 7, 12, 17, ...., 197, is equal to

Question

The sum of the common terms of the following three arithmetic progressions 3, 7, 11, 15, ...., 399; 2, 5, 8, 11, ...., 359 and 2, 7, 12, 17, ...., 197, is equal to ______.

Smart Achievers · Accepted Answer

(321)

$3, 7, 11, 15, \dots, 399 are in A.P.$

So, common difference $d_{1} = 7 - 3 = 4$

$2, 5, 8, 11, \dots, 359 are in A.P.$

Then, $d_{2} = 5 - 2 = 3; 2, 7, 12, 17, \dots, 197 are in A.P.$

$d_{3} = 7 - 2 = 5$

$L . C . M . of d_{1}, d_{2}, d_{3} = L . C . M . of (4, 3, 5) = 60$

On expanding all A.P.s, common terms are $47, 107, 167$

$∴$ $Sum = 47 + 107 + 167 = 321$

Solution

Q.
The sum of the common terms of the following three arithmetic progressions 3, 7, 11, 15, ...., 399; 2, 5, 8, 11, ...., 359 and 2, 7, 12, 17, ...., 197, is equal to ______.

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Solution

Q. The sum of the common terms of the following three arithmetic progressions 3, 7, 11, 15, ...., 399; 2, 5, 8, 11, ...., 359 and 2, 7, 12, 17, ...., 197, is equal to ______.

Ans. (321) 3, 7, 11, 15, …, 399 are in A.P. So, common difference d1=7-3=4 2, 5, 8, 11, …, 359 are in A.P. Then, d2=5-2=3; 2, 7, 12, 17, …, 197 are in A.P. d3=7-2=5 L.C.M. of d1,d2,d3=L.C.M. of (4,3,5)=60 On expanding all A.P.s, common terms are 47, 107, 167 ∴ Sum=47+107+167=321

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Q.
The sum of the common terms of the following three arithmetic progressions 3, 7, 11, 15, ...., 399; 2, 5, 8, 11, ...., 359 and 2, 7, 12, 17, ...., 197, is equal to ______.