Answer:
The common difference is 4
Step-by-step explanation:
Problem:
a1 = 16, an = 60, Sn = 456, n = ?, d = ?
First, we need to find n before we find d.
To find n we use this formula:
[tex]Sn = \frac{n}{2} (a1 + an)[/tex]
In this example, we have a1 = 16, an = 60, Sn = 456. After substituting these values to above formula, we obtain:
[tex]Sn = \frac{n}{2} (a1 + an)[/tex]
[tex]456 = \frac{n}{2} (16 + 60)[/tex]
[tex]2[/tex] · [tex]456[/tex] [tex]=[/tex] [tex]n[/tex] · [tex]76[/tex]
[tex]n = 12[/tex]
Now we finally found n which is n = 12.
The final step is, we need to find d.
To find d we use this formula:
[tex]Sn = \frac{n}{2} (2a1 + (n - 1) d)[/tex]
To find n = 12 we use this formula:
[tex]S12 = \frac{12}{2} (2a1 + (12 - 1) d)[/tex]
In this example, we have a1 = 16 and S12 = 456. After substituting these values to above formula, we obtain:
[tex]S12 = \frac{12}{2} (2a1 + (12 - 1) d)[/tex]
[tex]456 = \frac{12}{2} (2(16) + 11(d))[/tex]
[tex]\frac{2(456)}{12} = 32 + 11(d)[/tex]
[tex]76 = 32 + 11(d)[/tex]
[tex]d = \frac{76 - 32}{11}[/tex]
[tex]d = 4[/tex]