Question

Write the 1st, 2nd, 3rdand 18thterms for: A) Un= n2 + 4 B) Un = 6n + 5

Answer 1

(a)
`U_1 =5`;
`U_2 = 8`;
`U_(18) = 328`

(b)
`U_1 = 11`;
`U_2 =17`;
`U_(18) = 113`

Explanation:

Required

1st, 2nd and 18th terms

To do this, we simply substitute 1, 2 or 18 for n in the given equations

Solving (a):

`U_n =n^2 + 4`

1st term: n = 1

`U_1 =1^2 + 4`

`U_1 =1 + 4`

`U_1 =5`

2nd term: n = 2

`U_2 = 2^2 + 4`

`U_2 = 4 + 4`

`U_2 = 8`

18th term: n = 18

`U_(18) = 18^2 + 4`

`U_(18) = 324 + 4`

`U_(18) = 328`

Solving (b):

`U_n = 6n + 5`

1st term: n = 1

`U_1 = 6*1 + 5`

`U_1 = 6 + 5`

`U_1 = 11`

2nd term: n = 2

`U_2 = 6*2 + 5`

`U_2 =12 + 5`

`U_2 =17`

18th term: n = 18

`U_(18) = 6*18 + 5`

`U_(18) = 108 + 5`

`U_(18) = 113`