Question

What is the sum of the first 16 terms of the arithmetic sequence 11/5, 8/5 ,1, 2/5….. ?

Answer 1

Given

AP = 11/5 , 8/5 , 1 , 2/5 , ........

Find

Sum of first 16 terms

Step-by-step explanation

As we know the formula of sum of an AP

`s_n=(n)/(2)[a+(n-1)d]`

given a = 11/5

d = second term - first term

d = 8/5-11/5 = -3/5

n = 16

now, put values in formula

`\begin{gathered} s_(16)=(16)/(2)[(2*11)/(5)+(16-1)(-(3)/(5))] \\ s_(16)=8[(22)/(5)+15(-(3)/(5))] \\ s_(16)=8[(22)/(5)-9] \\ s_(16)=8[-(23)/(5)] \\ s_(16)=-(184)/(5) \\ \end{gathered}`

Final Answer

Sum of first 16 terms = -184/5