Question

Write an equation to describe the sequence below. Use n to represent the position of a termin the sequence, where n = 1 for the first term.-13, -25, -37,-49,..

Answer 1

Given

`-13,-25,-37,-49,\ldots`

It can be observed that the sequence is an arithmetic progression

Let our first term be a, and common difference be d

The common difference, d=

`\begin{gathered} d=T_2-T_1=T_3-T_2=T_4-T_3 \\ =-25-(-13)=-37-(-25)=-49-(-37) \\ =-25+13=-37+25=-49+37 \\ d=-12=-12=-12 \end{gathered}`

From the sequence given, a=-13

The nth term of an AP is given by the formula

`T_n=a+(n-1)d`

Substituting a and d will give

`\begin{gathered} T_n=-13+(n-1)-12 \\ =-13-12n+12 \\ =-13+12-12n \\ T_n=-1-12n \end{gathered}`

Hence, the equation to describe the sequence is Tn=-1-12n