Find the sum of the series.

Question

-2.02 - 2.11 - 2.2 - ... -4? 

Answer 1

The series - 2. 02 - 2.11 - 2.2 - ... - 4

The above series is arithmetic series.

common difference (d) = t₂ - t₁

d = - 2.11 - (- 2.02)

d = - 2.11 + 2.02

d = - 0.0 9

Formula for sum of sequence S_n = n/2(a + l)

Where a is first term and l is last term.

a = - 2.02.

 

Find the n value.

Formula for n^th term in a arithmetic series a_n = a + (n - 1)d

Substitute a = - 2.02 and d = - 0.09 in a_n.

- 4 = - 2.02 + (n - 1)(- 0.09)

- 4 = - 2.02 - 0.09n + 0.09

- 4 = - 1.93 - 0.09n

0.09n = - 1.93 + 4

0.09n = 2.07

n = (2.07)/(0.09)

n = 23

Now substitute n = 23, a = - 2.02 and l = - 4 in S_n.

S₂₃ = 23/2[- 2.02 + (- 4)]

= 11.5 (- 6.02)

S₂₃ = - 69.23.