# Arithmetic sequences and series

#### tmas

i have no idea how to even attempt a question like this....

Use the two given terms to find a, d, and tn for each arithmetic sequence

t5= 16 , t8=25

the answer should be a=4, d=3, tn=3n+1

help?

#### Prove It

MHF Helper
i have no idea how to even attempt a question like this....

Use the two given terms to find a, d, and tn for each arithmetic sequence

t5= 16 , t8=25

the answer should be a=4, d=3, tn=3n+1

help?
$$\displaystyle t_8 = t_5 + 3d$$

$$\displaystyle 25 = 16 + 3d$$

$$\displaystyle 9 = 3d$$

$$\displaystyle d = 3$$.

$$\displaystyle a = t_1 = t_5 - 4d$$

$$\displaystyle = 16 - 4(3)$$

$$\displaystyle = 4$$.

Since $$\displaystyle t_n = a + (n - 1)d$$

$$\displaystyle t_n = 4 + (n - 1)3$$

$$\displaystyle t_n = 4 + 3n - 3$$

$$\displaystyle t_n = 3n + 1$$.

HallsofIvy and tmas