If the tenth term of the sequence S = 1 + 5 + 13 + 29 + . … … . is k , then k 500 is equal to

Question

If the tenth term of the sequence S = 1 + 5 + 13 + 29 + . … … . is k , then k 500 is equal to,

MARKS App · Accepted Answer

S = 1 + 5 + 13 + 29 + . … … + t 9 + t 10 S = . … … 1 + 5 + 13 + . … … . + t 8 + t 9 + t 10 Subtracting we get 0 = 1 + 4 + 8 + 16 + . … … 9 t e r m s - t 10 ⇒ t 10 = 1 + 4 + 8 + 16 + . … . . 9 t e r m s = 1 + 4 1 - 2 9 1 - 2 = 1 + 4 2 9 - 1 = 1 + 4 512 - 1 = 2045 ⇒ k = 2045 ⇒ k 500 = 4.09

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