Question

What is the general rule for the sequence? 1.11, 2.54, 3.97, 5.40, ...

Answer 1

we are given

1.11, 2.54, 3.97, 5.40, ...

we can see that

first term is 1.11

now, we can find common difference

$d=2.54-1.11$

$d=1.43$

now, we can find second difference

$d=3.97-2.54$

$d=1.43$

we can see that

differences are same

so, this is arithematic sequence

now, we can find it's nth term

$a_n=a_1+(n-1)d$

$a_n=1.11+(n-1)*1.43$

now, we can simplify it

and we get

$a_n=1.43n-0.32$............Answer