Question

4a. Find the 120th term of the sequence: a1 = 5, d = 0.5 (3 marks) b. Find the sum of the first 120 terms of that sequence. (3 marks)

Answer 1

a₁₂₀ = 64.5 , S₁₂₀ = 4170

Explanation:

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 5 and d = 0.5 , then

a₁₂₀ = 5 + (119 × 0.5) = 5 + 59.5 = 64.5

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the sum to n terms of an arithmetic sequence is

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ] , then

S₁₂₀ =
`(120)/(2)` [ (2 × 5) + (119 × 0.5) ]

= 60(10 + 59.5)

= 60 × 69.5

= 4170