AMC10 2015 A

AMC10 2015 A · Q7

AMC10 2015 A · Q7. It mainly tests Arithmetic sequences basics.

How many terms are there in the arithmetic sequence 13, 16, 19, $\ldots$, 70, 73?

等差数列 13，16，19，$\ldots$，70，73 中一共有多少项？

(A) 20 20

(B) 21 21

(D) 60 60

(E) 61 61

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): The difference between consecutive terms is 3, and the difference between the first and last terms is $73-13=60=20\cdot 3$. Therefore the number of terms is $20+1=21$. Note: The $k$th term in the sequence is $3k+10$.

答案（B）：相邻两项的差是 3，首项与末项的差为 $73-13=60=20\cdot 3$。因此项数是 $20+1=21$。注：该数列的第 $k$ 项为 $3k+10$。

Topics

AR.012 Arithmetic sequences basics