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Sagot :
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
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