Question

the arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence

Answer 1

Given:

In an arithmetic sequence,

`a_1=2`

`a_i=a_(i-1)-3`

To find:

The sum of the first 335 terms in the given sequence.

Solution:

The recursive formula of an arithmetic sequence is:

`a_i=a_(i-1)+d` ...(i)

Where, d is the common difference.

We have,

`a_i=a_(i-1)-3` ...(ii)

On comparing (i) and (ii), we get

`d=-3`

The sum of first i terms of an arithmetic sequence is:

`S_i=(i)/(2)[2a+(i-1)d]`

Putting
`i=335,a=2,d=-3`, we get

`S_(335)=(335)/(2)[2(2)+(335-1)(-3)]`

`S_(335)=(335)/(2)[4+(334)(-3)]`

`S_(335)=(335)/(2)[4-1002]`

`S_(335)=(335)/(2)(-998)`

On further simplification, we get

`S_(335)=335* (-499)`

`S_(335)=-167165`

Therefore, the sum of the first 335 terms in the given sequence is -167165.