What is the sum of a 12-term arithmetic sequence where the last term is 13 and the common difference is -10?

605
660
748
816

Question

What is the sum of a 12-term arithmetic sequence where the last term is 13 and the common difference is -10?
 	
	605
	660
	748
	816

campbell_st · Answer

well you need to find the 1st term 

$$T_{n} = a + (n - 1)d$$

is the formula to find a term in an arithmetic series

You know  the 12th term = 13, the common difference is -10 and the number of terms n = 12

so 

$$13 = a + (12 -1) \times(-10)$$

solve for a. 

then the sum of the terms can be found using 

$$S_{n} = \frac{n}{2}[ a + l]$$

n = number of terms, a = 1st term and l = last term 

hope this helps.