Respuesta :

mhanifa

Answer:

  • The sum of the given sequence is 180

Step-by-step explanation:

Find each term

  • t₁ = 2*1 + 7 = 9
  • t₂ = 2*2 + 7 = 11
  • t₃ = 2*3 + 7 = 13
  • ...
  • t₉ = 2*9 + 7 = 25
  • t₁₀ = 2*10 + 7 = 27

The series is

  • 9, 11, 13, ..., 25, 27

The sum of series can be shown as

  • 9 + 11 + 13 + ... + 25 + 27

Find the sum

  • S₁₀ = 10/2*(9 + 27) = 5*36 = 180
semsee45

Answer:

180

Step-by-step explanation:

The given series means to sum the first 10 terms of the sequence [tex]a_t=2t+7[/tex]

[tex]\begin{aligned}\displaystyle \sum^{10}_{t=1}2t+7 & = (2 \cdot 1+7)+(2 \cdot 2+7)+...+(2 \cdot 9+7)+(2 \cdot 10+7)\\ & =2(1+2+...+9+10)+10(7)\\\\& = 2(1+2+...+9+10)+70\\\\ & = 2(55)+70\\\\& = 110+70\\\\ & = 180 \end{aligned}[/tex]

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