Respuesta :

jeni0905
It’s 76 because 6+6=12 and 12+10=22 so if you add 4 to the last one and you add the last number you get the next one. So, 22+14= 36 36+18= 54 so 18+4= 22 and 22+54= 76. Hope it helps!
fichoh

The sequence represents a quadratic function, the nth term of the sequence is 2n² + 4

The nth term of a quadratic sequence is :

  • an² + bn + c
  • c = zeroth term ; a = second difference ÷ 2

From the sequence :

First difference = 6, 10, 14, 18

Second difference = 4, 4, 4

First difference between terms in position 1 and 0 :

  • 6 - 4 = 2
  • Zeroth term = First term in sequence - 2 = 6 - 2 = 4

  • a = 4/2 = 2

Plugging the values into the equation :

2n² + bn + 4

Using the 2nd term :

  • n = 2

2(2)² + 2b + 4 = 12

8 + 2b + 4 = 12

2b = 12 - 12

2b = 0

b = 0

Hence, the nth term of the sequence is 2n² + 4

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