If t1 & t13 A.P 34&64 what is the value t10

In English please.

btw, I think I know what you are asking, but please use proper proper mathematical language

t10 = t1 + (t13-t1)/(13-1) * (10-1)

To find the value of t10 in the arithmetic progression (A.P.), we need to determine the common difference (d) between the terms.

The formula to find the nth term (tn) in an arithmetic progression is:
tn = a + (n-1)d

Given that t1 = 34 and t13 = 64, we can substitute these values into the formula to form two equations:

t1 = a + (1-1)d // First term, n = 1
t13 = a + (13-1)d // Thirteenth term, n = 13

Simplifying these equations, we get:
34 = a + 0d // d multiplied by 0 equals zero
64 = a + 12d

We can solve these equations to find the values of a and d.

From the first equation, we get:
a = 34

Substituting the value of a into the second equation, we have:
64 = 34 + 12d

Simplifying, we find:
12d = 30
d = 30/12
d = 2.5

Now that we know the common difference (d = 2.5), we can find t10 using the formula:
t10 = a + (10-1)d
= 34 + 9(2.5)
= 34 + 22.5
= 56.5

Therefore, the value of t10 in the arithmetic progression is 56.5.