Respuesta :

VirαtKσhli

Given :-

  • -13,-2,9,20,31 . . . . .

To find :-

  • which term in this sequence is 306 .

Solution :-

Common difference ,

  • d = 31 - 20
  • d = 11

As we know that ,

  • Tⁿ = a + (n-1)d
  • 306 = -13 + (n-1)11
  • 306+13 = (n-1)11
  • 319/11 = n-1
  • 29 = n -1
  • n = 30

Answer:

30th

Step-by-step explanation:

There is a common difference between consecutive terms, that is

- 2 - (- 13) = 9 - (- 2) = 20 - 9 = 31 - 20 = 11

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 13 and d = 11 , then

[tex]a_{n}[/tex] = - 13 + 11(n - 1) = - 13 + 11n - 11 = 11n - 24 ← equate to 306

11n - 24 = 306 ( add 24 to both sides )

11n = 330 ( divide both sides by 11 )

n = 30

The 30th term is 306

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