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In an A.P ,the first term is 2 and the sum of the first 5 terms is one fourth of the next five terms.Show that 20th term is -112. |
| First term = 2 Let d be the common difference of the A.P. Therefore, the A.P. is 2, 2 + d, 2 + 2d, 2 + 3d, … Sum of first five terms = 10 + 10d Sum of next five terms = 10 + 35d According to the given condition, 10 + 10 d = 1/4 (10 + 35d) 40 + 40d = 10 + 35d 30 = -5d d = -6 a20 = a+ (20 - 1)d = 2 + (19) (-6) = 2 - 114 = -112 Thus, the 20th term of the A.P. is –112. |
