# How do you write the first five terms of the arithmetic sequence given a_4=16, a_10=46?

Dec 22, 2017

$\left\{1 , 6 , 11 , 16 , 21 , . .\right\}$

#### Explanation:

the $n t h$ term of an AP is given by

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

we are given

${a}_{4} = 16 \implies 16 = {a}_{1} + 3 d - - - \left(1\right)$

${a}_{10} = 46 \implies 46 = {a}_{1} + 9 d - - \left(2\right)$

$\left(2\right) - \left(1\right)$

$30 = 6 d$

$\therefore d = 5$

taking $\left(1\right) \implies {a}_{1} = 16 - 3 \times 5 = 16 - 15 = 1$

mental check for (2), 1+9xx5=46sqrt

${a}_{1} = 1 , d = 5$

${a}_{1} = 1$

${a}_{2} = 6$

${a}_{3} = 11$

${a}_{4} = 16$

${a}_{5} = 21$

$\left\{1 , 6 , 11 , 16 , 21 , . .\right\}$