Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1= -34, d=-10?

1 Answer
Jul 17, 2015

Answer:

The explicit formula for the sequence is #color(red)( a_n = -10n-24)#, and the first five terms are #color(red)(-34, -44, -54, -64, -74)#.

Explanation:

We know that the common difference #d = -10#.

The general formula for an arithmetic sequence is

#a_n = a_1 + (n-1)d#.

So, for your sequence, the general formula is

#a_n = -34 + (n-1)(-10) = -34 -10n+10#

#a_n = -10n-24#

#a_1 = -34#

#a_2 = -10×2-24 = -20-24 = -44#

#a_3 = -10×3-24 = -30-24 = -54#

#a_4 = -10×4-24 = -40-24 = -64#

#a_5 = -10×5-24 = -50-24 = -74#

The first five terms are #-34, -44, -54, -64, -74#.