The sum 39

The sum of the first six terms of the arithmetic sequence is 72, and the second term is seven times the fifth term. Find the first term and the AP difference.

Correct answer:

a1 =  27
d =  -6

Step-by-step explanation:

s6=72 a2=7 a5  s6=6 a1+d (1+2+3+4+5) a1+d=7 (a1+4d) 72=6 a1+d (1+2+3+4+5) a1+d=7 (a1+4d)  72=6 a1+d (1+2+3+4+5) a1+d=7 (a1+4 d)  6a1+15d=72 6a1+27d=0  Row2Row1Row2 6a1+15d=72 12d=72  d=1272=6 a1=67215d=67215 (6)=27  a1=27 d=6   Verifying Solution:  a2=a1+d=27+(6)=21 a3=a2+d=21+(6)=15 a4=a3+d=15+(6)=9 a5=a4+d=9+(6)=3 a6=a5+d=3+(6)=3 s=a1+a2+a3+a4+a5+a6=27+21+15+9+3+(3)=72

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