Question

Write an equation for the nth term of the arithmetic sequence. Then find a30.

Answer 1

Answer:

Therefore the equation dor nth term is,

$a_{n} =a_{1} + (n-1)\times d$   and

$a_{30} =-18$

Step-by-step explanation:

Given:

Arithmetic Sequence as

11 , 10 , 9 , 8 , ..........

∴   First term     = a₁ = 11

   Second term = a₂ = 10

∴ Common Difference = d =  a₂ - a₁ = 10 - 11 = -1

∴ d = -1

To Find:

$a_{n} = ?\\and\\a_{30} = ?$

Solution:

An equation for the nth term of the arithmetic sequence is given by

$a_{n} =a_{1} + (n-1)\times d$

Substitute n= 30 for $a_{30}$ and a₁ and d we get

$a_{30} =11 + (30-1)\times -1\\\\a_{30} =11+29\times -1\\\\a_{30} =11-29\\\\a_{30} =-18\\\\\therefore a_{30} =-18\ \textrm{as required}$

Therefore,

$a_{30} =-18$