Series

Your task is express the sum of the following arithmetic series for n = 14:

S(n) = 11 + 13 + 15 + 17 + ... + 2n+9 + 2n+11

Correct answer:

S =  336

Step-by-step explanation:

$$\begin{gathered} a_1=11 \\ d=2 \\ {a}_n=11+2(n-1) \\ {S}_{14}=14\cdot {\displaystyle \frac{a_1+a_{14}}{2}}=14\cdot {\displaystyle \frac{11+37}{2}}=336 \end{gathered}$$

Try another example

Related math problems and questions:

• Mean
  if the mean of the set of data 5, 17, 19, 14, 15, 17, 7, 11, 16, 19, 5, 5, 10, 8, 13, 14, 4, 2, 17, 11, x is -91.74, what is the value of x?
• Sum of the seventeen numbers
  The sum of the 17 different natural numbers is 154. Determine the sum of the two largest ones.
• Sequence
  Write the first 6 members of this sequence: a₁ = 5 a₂ = 7 a_n+2 = a_n+1 +2 a_n
• Sequence
  In the arithmetic sequence is given: S_n=2304, d=2, a_n=95 Calculate a₁ and n.
• Numbers
  Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
• Cancel fractions
  Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
• To improper fraction
  Change mixed number to improper fraction a) 1 2/15 b) -2 15/17
• Tennis aces
  The number of aces served by Novak Djokovic in the last 20 tournaments that he has participated in, is shown below. 12 17 13 7 8 14 11 14 10 12 15 9 11 13 6 15 18 5 19 24 1.1 using the raw, determine the range. 1.2 Group the data into a frequency distribu
• Reciprocal
  What is the reciprocal of the sum of the reciprocals of 7 and 6?
• Arithmetic progression 2
  The 3rd term of an Arithmetic progression is ten more than the first term, while the fifth term is 15 more than the second term. Find the sum of the 8th and 15th terms of the Arithmetic progression if the 7th term is seven times the first term.
• Speed of Slovakian trains
  Rudolf decided to take the train from the station 'Ostratice' to 'Horné Ozorovce'. In the train timetables found train Os 5409 : km 0 Chynorany 15:17 5 Ostratice 15:23 15:23 8 Rybany 15:27 15:27 10 Dolné Naštice 15:31 15:31 14 Bánovce nad Bebravou 15:35 1
• Prism
  The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
• Two forces
  The two forces F1 = 580N and F2 = 630N, have an angle of 59 degrees. Calculate their resultant force, F.
• Sign of a expression
  What is the sign of expression: minus 18 start fraction 9 divided by 17 end fraction plus left parenthesis minus 18 start fraction 9 divided by 17 end fraction right parenthesis?
• Forces
  Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
• Sum of members
  What is the sum of the first two members of the aritmetic progression if d = -4.3 and a3 = 7.5?
• Sum of 20
  Sum of the two numbers is 15 1/6. If one of the numbers is 2 2/3, find the other number.