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The sum of the common terms of the following three arithmetic progressions. 3,7,11,15,…………,3993,7,11,15,…………,399 2,5,8,11,.........3592,5,8,11,.........359  and 2,7,12,17,……,1972,7,12,17,……,197, is equal to _____ .
Asked by chiyalaxmi28 | 18 Mar, 2023, 10:34: AM
answered-by-expert Expert Answer
First A.P. is 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, …………,399 
First term (a1) = 3, common difference (d1) = 4
 
Second A.P. is 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, .........359
First term (a2) = 2, common difference (d2) = 3
 
Third A.P. is 2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52……,197
First term (a3) = 2, common difference (d3) = 5
 
LCM(d1, d2, d3) = LCM(4, 3, 5) = 60
The common terms of the three APs are 47, 107, 167
Sum of these term = 47+107+167 = 321
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