What is the first, fourth, and tenth terms of the arithmetic sequence #A(n) = -6 + (n-1)(?6)#?

1 Answer
Mar 17, 2018

Answer:

a) First Term #color(red)(a_1 = -6#

b) Fourth term #color(blue)(a_4 = -6 + (4-1) * 6 = 12#

c) Tenth Term #color(green)(a_(10) = -6 + (10-1) * 6 = 48#

Explanation:

#A_n = -6 + (n-1) * 6# Eqn (1)

Standard for of an Arithmetic Sequence for the #n^(th)# term is given by the formula,

#A_n = A_1 + (n-1) * d# Eqn (2),

where #a_1 # first term & #d# the common difference.

Comparing Eqns (1), (2)

#a_1 = -6, d = 6#

a) First Term #a_1 = -6#

b) Fourth term #a_4 = -6 + (4-1) * 6 = -6 + (3 * 6) = 12#

c) Tenth Term #a_(10) = -6 + (10-1) * 6 = -6 + 54 = 48#