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2 votes
2 votes
What is the sum of the first 30 terms of this arithmetic sequence?
6,13, 20, 27, 34, ...

User Mr Mo
by
2.8k points

2 Answers

17 votes
17 votes

Answer:

  • The sum of the first 30 terms of this arithmetic sequence is 209. Hoped this helped.

Explanation:

We know that:

  • Formula = 6 + (7x)

Work:

  • => 6 + (7x)
  • => 6 + {7(29)}
  • => 6 + 203
  • => 209

Hence, the sum of the first 30 terms of this arithmetic sequence is 209. Hoped this helped.


BrainiacUser1357

User Mathias Vonende
by
2.8k points
30 votes
30 votes

Answer:

The sum of first 30 terms of arithmetic sequence is 3225.

Step-by-step explanation:

Here's the required formula to find the sum of the arithmetic sequence :


\star{\underline{\boxed{\sf{S_n = (n)/(2)\Big[2a + (n - 1)d\Big]}}}}


  • \pink\star Sₙ = number of terms of AP

  • \pink\star n = n terms of AP

  • \pink\star d = common difference of AP

  • \pink\star a = first term of AP

Substituting all the given values in the formula to find the sum of arithmetic sequence :


  • \blue\star Sₙ = 30

  • \blue\star n = 30

  • \blue\star d = 7

  • \blue\star a = 6


{\implies{\sf{S_n = (n)/(2)\Big[2a + (n - 1)d\Big]}}}


{\implies{\sf{S_(30) = (30)/(2)\Big[2 * 6 + (30 - 1)7\Big]}}}


{\implies{\sf{S_(30) = (30)/(2)\Big[12+ (29)7\Big]}}}


{\implies{\sf{S_(30) = (30)/(2)\Big[12+ 29 * 7\Big]}}}


{\implies{\sf{S_(30) = (30)/(2)\Big[12+203\Big]}}}


{\implies{\sf{S_(30) = (30)/(2)\Big[ \: 215 \: \Big]}}}


{\implies{\sf{S_(30) = 15\Big[ \: 215 \: \Big]}}}


{\implies{\sf{S_(30) = 15 * 215}}}


{\implies{\sf{S_(30) = 3225}}}


\star{\underline{\boxed{\sf{S_(30) =3225}}}}

Hence, the sum of first 30 terms of arithmetic sequence is 3225.


\rule{300}{2.5}

User Jordan Thornquest
by
2.8k points
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