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

Mar 17, 2018

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:

${A}_{n} = - 6 + \left(n - 1\right) \cdot 6$ Eqn (1)

Standard for of an Arithmetic Sequence for the ${n}^{t h}$ term is given by the formula,

${A}_{n} = {A}_{1} + \left(n - 1\right) \cdot d$ 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 ${a}_{4} = - 6 + \left(4 - 1\right) \cdot 6 = - 6 + \left(3 \cdot 6\right) = 12$

c) Tenth Term ${a}_{10} = - 6 + \left(10 - 1\right) \cdot 6 = - 6 + 54 = 48$