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Let n be the number of terms...............a--> first term.....d-->common difference... L--->Last term 12 th term forward......= a + 11d 9th term backward.........Now considering the sereis backward.....Thus backward series has first term as L and common difference as (-d)............. 9th term back ward...........= L + 8(-d) Therfore.............. L - 8d = a + 11d Thus............ (L-a) = 19d.................(1) Now ......... L = a + (n-1)d....... Putting in............(1)......... (n-1)d = 19d Thus.............. n-1 = 19 Thus n = 20 |
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