Question

Find the general term of the following sequence:

6, 24, 60, 120, 210, 336, 504, ...
Please show your work too. Thank you!​

Answer 1

The general term is (n)(n+1)(n+2).

Explanation:

Term 1 = 6 = (1)(2)(3)

Term 2 = 24 = (2)(3)(4)

Term 3 = 60 = (3)(4)(5)

Term 4 = 120 = (4)(5)(6)

Term 5 = 210 = (5)(6)(7)

Term 6 = 336 = (6)(7)(8)

Term 7 = 504 = (7)(8)(9)

So, term n = (n)(n+1)(n+2).

Answer 2

The formula is

`\boxed{\star{\sf a_n=n(n+1)(n+2)}}`

Lets verify

`\\ \sf\longmapsto a_1=1(1+1)(1+2)=2(3)=6\checkmark`

`\\ \sf\longmapsto a_2=2(2+1)(2+2)=2(3)(4)=6(4)=24\checkmark`

`\\ \sf\longmapsto a_3=3(3+1)(3+2)=3(4)(5)=12(5)=60`

`\\ \sf\longmapsto a_4=4(4+1)(4+2)=4(5)(6)=20(6)=120`

`\\ \sf\longmapsto a_5=5(5+1)(5+2)=5(6)(7)=30(7)=210`

`\\ \sf\longmapsto a_6=6(6+1)(6+2)=6(7)(8)=42(8)=336`

`\\ \sf\longmapsto a_7=7(7+1)(7+2)=7(8)(9)=56(9)=504`

Hence verified

Lets take any value of n

• Let it be 100

`\\ \sf\longmapsto a_(100)=100(100+1)(100+2)=100(101)(102)=1030200`