i am stuck at a question that is asking for the common difference, first term, and general term for the arithmetic sequence the question is

t10=50 and t27=152

i found my d=6 and t1=(-4) so know my equation is: tn=(-4)+(n-1)6 i had asken my teacher to tell me what the general term is and he told me its tn=6n-10.I have tried to get to the answer but i don't know how please help

If tn = -4 + (n-1)6

then
tn = -4 + 6 n - 6
or
tn = 6 n - 4 -6
which is
6 n - 10 sure enough

thank you

You are welcome.

To find the general term for an arithmetic sequence, you need to first determine the common difference (d) and the first term (t1), as you have correctly done.

You calculated the common difference (d) as 6, and the first term (t1) as -4. With these values, you can then use the formula for the general term of an arithmetic sequence, which is:

tn = t1 + (n-1)d

Substituting the values you have:

tn = -4 + (n-1)6

Now, let's simplify this expression step by step:

tn = -4 + 6n - 6

Next, combine like terms:

tn = 6n - 10

So, the general term for the given arithmetic sequence is tn = 6n - 10.

Now that you have the general term, you can use it to find any specific term in the sequence simply by plugging in the value of n. For example, if you want to find the 10th term (t10), substitute n = 10 into the general term equation:

t10 = 6(10) - 10
t10 = 60 - 10
t10 = 50 (which matches what you were given)

Similarly, you can find the 27th term (t27):

t27 = 6(27) - 10
t27 = 162 - 10
t27 = 152 (which also matches what you were given)

So, the general term tn = 6n - 10 correctly describes the arithmetic sequence.