Question

A sequence is defined by the recursive formula a₁=-6 and aₙ=aₙ₋₁+2n. Write out the next three terms of this sequence. Show the work that leads to your terms.

Answer 1

To find the next terms in the sequence, use the given recursive formula. Substitute n=2, n=3, and n=4 into the formula to find a₂, a₃, and a₄ respectively.Finally, substitute n=4: a₄=a₄₋₁+2(4)=4+8=12.

Step-by-step explanation:

The sequence is defined by the recursive formula a₁=-6 and aₙ=aₙ₋₁+2n. To find the next three terms, we can use the formula. Start by substituting n=2 into the formula: a₂=a₂₋₁+2(2)=-6+4=-2. Next, substitute n=3: a₃=a₃₋₁+2(3)=-2+6=4. Finally, substitute n=4: a₄=a₄₋₁+2(4)=4+8=12.