Question

Given that nth term of an arithmetic progression is Tn=7-2n, find a)second term b)common difference ?? Help pls!!

Answer 1

The second term of the arithmetic sequence is `color(blue)(3)`, and the common difference is `color(red)(-2)`.

Explanation:

It is given that the `n`th term of an arithmetic sequence is given as `T_n=7-2n`.

To find the second term, just substitute `n=2`:
`T_2=7-2*2=color(blue)(3)`

The common difference is defined as the number `T_(n+1)-T_n`, essentially the difference between a term and the previous term. We know that `T_(n+1)=7-2(n+1)=5-2n` and `T_n=7-2n`, so the common difference is
`T_(n+1)-T_n=(5-2n)-(7-2n)=color(red)(-2)`

Note that, since the common difference is negative, the arithmetic sequence is decreasing, i.e. the successive terms are smaller than the previous terms.

Answer 2

`a_2=3" and "d=-2`

Explanation:

`"to find the second term, substitute n = 2 into"`
`"the n th term formula"`

`rArra_2=7-(2xxcolor(red)(2))=7-4=3`

`"the common difference d is given as "`

`d=a_2-a_1=a_3-a_2=...... =a_n-a_(n-1)`

`"find the third term "`

`rArra_3=7-(2xxcolor(red)(3))=7-6=1`

`rArrd=a_3-a_2=1-3=-2`