# What is the 35th term of the arithmetic sequence where a1 = 13 and a17 = –51?

Aug 27, 2015

color(blue)(a_35= -123

#### Explanation:

The data given is :
${a}_{1} = 13$
${a}_{17} = - 51$

The formula for $n t h$ term is:
color(blue)(a_n = a_1+(n-1)d

Applying the same:
${a}_{17} = {a}_{1} + \left(17 - 1\right) \cdot d$

$- 51 = 13 + 16 d$

$16 d = - 64$

color(blue)(d=-4

Now,
${a}_{35} = {a}_{1} + \left(35 - 1\right) \cdot d$

$= 13 + 34 . \left(- 4\right)$

$= 13 - 136$

color(blue)(a_35= -123