Question

an为等差数列,a4+a7+a10=17,a4+a5+a6...+a14=77,ak=13,求k

Answer 1

若m+n=p+q则am+an=ap+aq;

a4+a10=2a7 则3a7=17;a7=17/3;

a4+a5+a6+···+a14=10*a9+a9=11a9=77 则a9=7；

a9-a7=2d=7-17/3=4/3

d=2/3;a1=5/3

ak=a1+(k-1)d=5/3+(k-1)*2/3=13

k=18

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