Find the 7th term of 2(sqrt{5}), 4(sqrt{5}), 6(sqrt{5}), ...

bruinhemd3ji

bruinhemd3ji

Answered question

2022-11-10

Find the 7th term of 2(sqrt{5}), 4(sqrt{5}), 6(sqrt{5}), ...

Answer & Explanation

Cullen Petersen

Cullen Petersen

Beginner2022-11-11Added 13 answers

Let the given seq. be { t n } 1 = { 2 5 , 4 5 , 6 5 , ... }
Then, t 2 - t 1 = 2 5 , t 3 - t 2 = 2 5 , ...
Assuming that the pattern continues , we find that the seq. is an A.P.,
with, t 1 = 2 5 , and, common difference d = 2 5
t n = t 1 + ( n - 1 ) d = 2 5 + ( 2 5 ) ( n - 1 ) = ( 2 5 ) ( 1 + n - 1 ) = ( 2 5 ) n
Hence, the reqd. term = t 7 = ( 2 5 ) 7 = 14 5

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