Common difference

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

Correct result:

d =  -9.3333

Solution:

a4=6 a8+a9=−72 (a4+4d)+(a4+5d)=−72  2a4+9d=−72  d=(−72−2⋅ a4)/9=(−72−2⋅ 6)/9=−283≐−9.3333=−9.3333   Verifying Solution:  a1=a4−3⋅ d=6−3⋅ (−9.3333)=34 k8=a1+7⋅ d=34+7⋅ (−9.3333)=−943≐−31.3333 k9=a1+8⋅ d=34+8⋅ (−9.3333)=−1223≐−40.6667 s89=k8+k9=(−31.3333)+(−40.6667)=−72

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