Answer:
The equation for the nth term of the given arithmetic sequence is: [tex]\mathbf{a_n=13n+22}[/tex]
Step-by-step explanation:
We need to write an equation for the nth term of the arithmetic sequence:
15,28,41 ....
The equation for arithmetic sequence is: [tex]a_n=a_1+(n-1)d[/tex]
Where [tex]a_n[/tex] is the nth term, [tex]a_1[/tex] is first term and d is common difference
In the given sequence we have:
a₁ = 15
a₂ = 28
We can find common difference using the formula:
[tex]a_n=a_1+(n-1)d\\Put\: n=2, a_2=28\: and\: a_1=15\\a_2=a_1+(2-1)d\\28=15+d\\d=28-15\\d=13[/tex]
So, the common difference d is 13
Now, equation for nth term will be:
[tex]a_n=a_1+(n-1)d\\Put\:a_1=15, d=13\\a_n=15+(n-1)13\\Solving:\\a_n=15+13n-13\\a_n=13n+2[/tex]
So, the equation for the nth term of the given arithmetic sequence is: [tex]\mathbf{a_n=13n+22}[/tex]
where n=1,2,3..
