Answered

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(a) 1; 4; 9; 16; ....
Rule:
Missing numbers:
(b) 2; 13; 26; 49
Rule:
Missing numbers:
(c) 4; 14; 26; 49;
Rule:
Missing numbers:
(d) 1; 8; 27; 64;
Rule:
​

Sagot :

reinhard10158

Step-by-step explanation:

(a) 1, 4, 9, 16, ...

1², 2², 3², 4², ...

rule : x²

next number : 5² = 25

(b) I think you made a typo here.

the given sequence should be

2, 13, 26, 41, ... correct ?

2 = (1+4)² - 23 = 25 - 23

13 = (2+4)² - 23 = 36 - 23

26 = (3+4)² - 23 = 49 - 23

41 = (4+4)² - 23 = 64 - 23

rule : (x + 4)² - 23

next number : (5+4)² - 23 = 9² - 23 = 81 - 23 = 58

(c) I think you made here a typo too.

the given sequence should be

4, 14, 29, 49, ... correct ?

4 = (5×1² + 5×1 - 2)/2 = (5+5-2)/2 = 8/2

14 = (5×2² + 5×2 - 2)/2 = (20 + 10 - 2)/2 = 28/2

29 = (5×3² + 5×3 - 2)/2 = (45 + 15 - 2)/2 = 58/2

49 = (5×4² + 5×4 - 2)/2 = (80 + 20 - 2)/2 = 98/2

rule : (5×x² + 5×x - 2)/2

next number : (5×5² + 5×5 - 2)/2 = (125 + 25 - 2)/2 =

= 148/2 = 74

(d) 1, 8, 27, 64, ...

1³, 2³, 3³, 4³, ...

rule : x³

next number : 5³ = 125

I could not find any rules for the (b) and (c) as you listed them.

other options for corrections :

2, 13, 26, 51, ...

+11, +13, +15, +17, ...

leading to 68 as next number.

4, 14, 26, 40, ...

+10, +12, +14, +16, ...

leading to 56 as next number.

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