5, 7, 17, 47, 115, ? | vedclass

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Question

(B) Let the given series be $5, 7, 17, 47, 115, x$.Calculate the differences between consecutive terms:$7 - 5 = 2$$17 - 7 = 10$$47 - 17 = 30$$115 - 47

Vedclass · Accepted Answer

$245$

Vedclass · Answer

(B) Let the given series be $5, 7, 17, 47, 115, x$.Calculate the differences between consecutive terms:$7 - 5 = 2$$17 - 7 = 10$$47 - 17 = 30$$115 - 47 = 68$Now,find the second level of differences:$10 - 2 = 8$$30 - 10 = 20$$68 - 30 = 38$Now,find the third level of differences:$20 - 8 = 12$$38 - 20 = 18$Observe the pattern in the third level of differences: $12, 18$. The difference increases by $6$ each time. So,the next difference in the third level should be $18 + 6 = 24$.Now,work backwards to find $x$:Next second level difference $= 38 + 24 = 62$.Next first level difference $= 68 + 62 = 130$.Therefore,$x = 115 + 130 = 245$.

$5, 7, 17, 47, 115, ?$

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