An arithmetic is defined as: 100 + 93 + 86 + .... Write down the 24th term and the sum of of the first 30 terms.

Question

An arithmetic is defined as: 100 + 93 + 86 + ....

 

Write down the 24th term and the sum of of the first 30 terms. 

Answer 1

a_n = 100 + (n - 1)(-7)

a₂₄ = 100 + 23(-7)

a₂₄ = 100 - 161

a₂₄ = -61

 

S₃₀ = (30/2)(2(100) + (30 - 1)(-7))

S₃₀ = 15(200 - 203)

S₃₀ = -45