CBSE Class 10 Answered

Check whether forms an Arithmetic progression or not .If it is an AP then write the common difference and the next two terms.

Asked by Topperlearning User | 21 Sep, 2017, 02:21: PM

Expert Answer

$begin mathsize 12px style Here comma space straight a subscript 1 space equals space 6 comma space straight a subscript 2 space equals space 6 space minus space square root of 2 We space have comma space straight a subscript 2 space minus space space straight a subscript 1 space equals space 6 space minus space square root of 2 space minus space 6 space equals space minus space square root of 2 straight a subscript 3 space minus space space straight a subscript 2 space equals space 6 space minus space 2 space square root of 2 space minus open parentheses space space 6 space minus space square root of 2 space close parentheses space space space space space space space space space space space space space space space space space equals space space 6 space minus space 2 space square root of 2 space minus space 6 space plus space square root of 2 space space space space space space space space space space space space space space space space space equals space minus space 2 space square root of 2 space plus space square root of 2 space equals space minus space square root of 2 straight a subscript 4 space minus space space straight a subscript 3 space end subscript equals space 6 space minus space 3 square root of 2 space minus space open parentheses space space 6 space minus space 2 square root of 2 space close parentheses space space space space space space space space space space space space space space space space space equals space 6 space minus space 3 square root of 2 space space minus space 6 space plus space 2 square root of 2 space space space space space space space space space space space space space space space space space equals negative space 3 square root of 2 space plus space 2 square root of 2 space equals negative space square root of 2 that space is comma space straight a subscript straight k plus 1 end subscript space minus space straight a subscript straight k space space is space constant comma space so space this space series space is space an space Arithmetic space Progression. The space next space two space terms space will space be comma straight a subscript 5 space equals space straight a subscript 4 space plus space straight d space space space space space space equals space 6 space minus space 3 square root of 2 space plus space open parentheses negative space square root of 2 close parentheses space space space space space space equals 6 space minus space 4 square root of 2 space straight a subscript 6 space equals space straight a subscript 5 space plus space straight d space space space space space space space equals 6 space minus space 4 square root of 2 space plus space open parentheses negative space square root of 2 close parentheses space space space space space space space space equals space 6 space minus space 5 square root of 2 space space end style$