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Consider the arithmetic sequence 171, 167, 163,……….. (i) Is ‘0’ is a term of this sequence? Why? (ii) How many positive terms are in this sequence? |
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Answer» Arithmetic senes : 171, 167, 163 ……………. i. Here common difference d = x2 - x1 = 167 - 171 = -4 Obtaining 0 as a term of this sequence 0 - 171 = -171 is a multiple of common difference -4. -171/-4 = 171/4 Quotient = 42, Remainder = 3 Remainder is not zero, so -171 is not a multiple of common difference -4. ∴ 0 will not be a term of the sequence ii. Remainder = 3, ∴ 0 + 3 = 3 is a term of the sequence. ∴ 3 is the last positive term of the sequence. ∴ Sum of positive terms of the sequence = \(\frac{x_n-x_1}{d}+1=\frac{3-171}{-4}+1\) = (-168/-4) + 1 = 42 + 1 = 43 |
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