How do you write the first five terms of the arithmetic sequence given a_1=2, a_12=46?

Sep 3, 2017

$\left\{2 , 6 , 10 , 14 , 18\right\}$

Explanation:

to write the first five terms we need to know

$\left(1\right) \text{ }$the first term$\text{ } {a}_{1}$

$\left(2\right) \text{ }$ the common difference $d$

we know$\text{ } {a}_{1} = 2$

we also know

${a}_{12} = 46.$

For an AP the ${n}^{t h}$term is given by

${a}_{n} = a + \left(n - 1\right) d$

$\therefore {a}_{12} = 46 = 2 + 11 d$

$11 d = 46 - 2 = 44$

$\implies d = 4$

so we have

${a}_{1} = 2$

${a}_{2} = 2 + 4 = 6$

${a}_{3} = 6 + 4 = 10$

${a}_{4} = 10 + 4 = 14$

${a}_{5} = 14 + 4 = 18$