Question

please help me for the brainliest answer

Answer 1

Answer:

aₙ= -2n²

Step-by-step explanation:

Solution 1:

The sequence:

• -2, -8, -18, -32, -50

The difference between the terms:

• -6, -10, -14, -18

• a₁= -2
• a₂= a₁ - 6 = a₁ - 2*3= a₁- 2*(2²-1)
• a₃= a₂ - 10 = a₁ - 16= a₁ - 2*8= a₁ - 2*(3²-1)
• a₄= a₃- 14= a₁ - 30= a₁ - 2*15= a₁ - 2*(4² -1)
• ...
• aₙ= a₁ -2*(n²-1)= -2 -2n² +2= -2n²

As per above, the nth term is: aₙ= -2n²

Solution 2

The sequence:

• -2, -8, -18, -32, -50
• -2*1, -2*4, - 2*9, -2*25
• -2*1², -2*2², -2*3², -2*4², -2*5², ..., -2*n²
• aₙ= -2n²