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 | 21st 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

Answered by  | 21st Sep, 2017, 04:21: PM