2014
Mathematics
67ca00ce0c643c71d77dee1f
What is the common ratio of the G.P. (√10 + √5) + (√10 +2√5) +...?
A.
√2
B.
√5
C.
3
D.
5
Correct Answer: √2
Explanation
Common ratio r of the G.P is r = Tn + 1/Tn = Tn/Tn r = √10 +2√5/√10 + √5 r = (√10 + 2√5)/(√10 + √5) × (√10 − √5)/(√10 − √5) =(√10)(√10)+(√10)(−√5) + (2√5)(√10) + (2√5)(−√5)/(√10)2−(√5)2 10−√50 + 2√50 −10/10−5 √50/5 √25 x 2/5 5√2/5 √2
Common ratio r of the G.P is r = Tn + 1/Tn = Tn/Tn r = √10 +2√5/√10 + √5 r = (√10 + 2√5)/(√10 + √5) × (√10 − √5)/(√10 − √5) =(√10)(√10)+(√10)(−√5) + (2√5)(√10) + (2√5)(−√5)/(√10)2−(√5)2 10−√50 + 2√50 −10/10−5 √50/5 √25 x 2/5 5√2/5 √2THIS WEEK's
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