Common difference

The 4th term of an arithmetic progression is 6. If the sum of the 8th and 9th terms is -72, find the common difference.

Correct answer:

d =  -9.3333

Step-by-step explanation:

$$\begin{gathered} a_4=6 \\ {a}_8+a_9=-72 \\ (a_4+4d)+(a_4+5d)=-72 \\ 2a_4+9d=-72 \\ d=(-72-2\cdot a_4)\mathrm{/}9=(-72-2\cdot 6)\mathrm{/}9=-{\displaystyle \frac{28}{3}}=-9\frac{1}{3}\doteq -9.3333=-9.3333 \\ \text{ Verifying Solution: } \\ {a}_1=a_4-3\cdot d=6-3\cdot (-9.3333)=34 \\ {k}_8=a_1+7\cdot d=34+7\cdot (-9.3333)=-{\displaystyle \frac{94}{3}}=-31\frac{1}{3}\doteq -31.3333 \\ {k}_9=a_1+8\cdot d=34+8\cdot (-9.3333)=-{\displaystyle \frac{122}{3}}=-40\frac{2}{3}\doteq -40.6667 \\ {s}_{89}=k_8+k_9=(-31.3333)+(-40.6667)=-72 \end{gathered}$$

Try another example

Related math problems and questions:

• 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.
• Geometric progressiob
  If the sum of four consective terms of geometric progression is 80 and arithmetic mean of second and fourth term is 30 then find terms?
• If the 3
  If the 6th term of a GP is 4 and the 10th is 4/81, find common ratio r.
• In the 8
  In the A. P. 36, 39, 42, …, which term is 276?
• Sum 1-6
  Find the sum of the geometric progression 3, 15, 75,… to six terms.
• What is 10
  What is the 5th term, if the 8th term is 80 and common ratio r =1/2?
• GP - three members
  The second and third of a geometric progression are 24 and 12(c+1), respectively, given that the sum of the first three terms of progression is 76. determine the value of c.
• Fifth member
  Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.
• Difference AP
  Calculate the difference of arithmetic progression if the sum of its first 19 members Sn = 8075 and the first member is a₁ = 20
• Negative difference
  Find four arithmetic progression members between 7 and -6.
• 6 terms
  Find the first six terms of the sequence. a1 = 7, an = an-1 + 6
• Sum of GP members
  Determine the sum of the GP 30, 6, 1.2, to 5 terms. What is the sum of all terms (to infinity)?
• HP - harmonic progression
  Determine the 8th term of the harmonic progression 2, 4/3, 1,…
• HP - harmonic progression 2
  Compute the 16th term of the HP if the 6th and 11th term of the harmonic progression are 10 and 18 respectively.
• Determine AP
  Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71
• AS sequence
  In an arithmetic sequence is given the difference d = -3 and a₇₁ = 455. a) Determine the value of a₆₂ b) Determine the sum of 71 members.
• Find the 19
  Find the 1st term of the GP ___, -6, 18, -54.