Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1 = 39, d=-5?

1 Answer
Aug 31, 2015

Answer:

The first five terms are: # 39, 34,29,24,19#
and
#color(blue)(a_n=34-5n# for #n=1,2,3....#

Explanation:

The first number of the sequence is
#a_1 =39#
and the common difference is
#d=-5#

All subsequent terms for the arithmetic sequence can be found by simply adding the common difference to the preceding term.
#a_2 = a_1 +d = 39 +(-5)#
#a_2 = 34#
#a_3 = a_2 +d = 34 +(-5) = 29#
#a_4 = a_3 +d = 29+(-5) =24#
#a_5 =a_4 +d= 24 +(-5)=19#

The explicit formula is
#a_n = a_1+(n-1)d#
#a_n=39+(n-1)* (-5)#
#a_n=39-5n-5#
#color(blue)(a_n=34-5n# (for #n=1,2,3....#)