Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1 = 35, d=4?

1 Answer
Jul 17, 2015

Answer:

The explicit formula for the sequence is #color(red)( a_n = 4n+31)#, and the first five terms are #color(red)( 35,39,43,47,51)#.

Explanation:

We know that the common difference #d = 4#.

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 = 35 + 4(n-1) = 35 +4n-4#

#a_n = 4n+31#

#a_1 = 35#

#a_2 = 4×2+31 = 8+31 = 39#

#a_3 = 4×3+31 = 12+31 = 43#

#a_4 = 4×4+31 = 16+31= 47#

#a_5= 4×5+31 = 20+31 = 51#

The first five terms are #35,39,43,47,51#.