Question

Find the next term in the series
19 40 144 684 1004 1754 ?

Answer 1

Question :- Find the next term in the series

19 40 144 684 1004 1754 ?

Solution :-

checking the difference between given terms we get,

→ 40 - 19 = 21

→ 144 - 40 = 104

→ 684 - 144 = 540

→ 1004 - 684 = 320

→ 1754 - 1004 = 750

as we can see that, difference between given terms is in random order. using difference of difference method we get,

→ 104 - 21 = 83

→ 540 - 104 = 436

→ 320 - 540 = (-220)

→ 750 - 320 = 430

again finding the difference of difference now,

→ 436 - 83 = 353

→ (-220) - 436 = (-656)

→ 430 - (-220) = 650

again finding the difference of difference now,

→ (-656) - (353) = (-1009)

→ 650 - (-656) = 1306

again finding the difference of difference now,

→ 1306 - (-1009) = 2315 .

using this last difference as same in next terms now, we get,

→ 1306 + 2315 = 3621

→ 650 + 3621 = 4271

→ 430 + 4271 = 4701

→ 750 + 4701 = 5451

→ 1754 + 5451 = 7205 (Ans.)

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