Respuesta :

Step-by-step explanation:

Given:

  • 313 is the nth term of the sequence 8, 13, 18.

[tex]\\[/tex]

To Find:

  • nth term of the sequence

[tex]\\[/tex]

Solution:

AP series : 8,13,18...

Here,

  • a = 8
  • d = 13 - 8 = 5
  • [tex]\rm a_{n}[/tex] = 313

[tex]\\[/tex]

We know that,

[tex]\\[/tex]

[tex]\dashrightarrow \: \: \: {\underline{\boxed{\purple{\pmb{\mathfrak{a_{n} = a + (n - 1)d}}}}}} \\ \\ [/tex]

[tex]\dashrightarrow \rm \: \: \: 313 = 8 + (n -1) 5 \\ \\ [/tex]

[tex]\dashrightarrow \rm \: \: \: 313 - 8 = (n - 1)5 \\ \\ [/tex]

[tex]\dashrightarrow \rm \: \: \: 305 = (n - 1)5 \\ \\ [/tex]

[tex]\dashrightarrow \rm \: \: \: \dfrac{305}{5} = n - 1 \\ \\ [/tex]

[tex]\dashrightarrow \rm \: \: \: 61 = n - 1 \\ \\ [/tex]

[tex]\dashrightarrow \rm \: \: \: 61 + 1 = n \\ \\ [/tex]

[tex]\dashrightarrow \: \: \: {\underline{\boxed{\purple{\pmb{\mathfrak{62 = n}}}}}} \\ \\ [/tex]

Hence,

  • Value of n is 62