Question

Give the form of Tn= , from this sequence 3 , 8 ,13 , 18 , 23 , 28 , 33 , 38​

Answer 1

`T_n=5n-2`

Explanation:

This is an arithmetic sequence with first term 3 and common difference 5.

Using the formula for the explicit formula of an arithmetic sequence,
`T_n =3+5(n-1)=5n-2`

Answer 2

`T_(n)` = 5n - 2

Explanation:

there is a common difference between consecutive terms , that is

8 - 3 = 13 - 8 = 18 - 13 = 23 - 18 = 28 - 23 = 33 - 28 = 38 - 33 = 5

this indicates the sequence is arithmetic with nth term

`T_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 3 and d = 5 , then

`T_(n)` = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2