Question

Find the sum of the first 31 terms of the following series, to the nearest integer5,14,23

Answer 1

Step 1

Given;

`The\text{ series; 5,14,23}`

Required; To find the sum of the first 31 terms

Step 2

The series is arithemtic, hence the common difference(d) will be

`\begin{gathered} T_2-T_1=14-5=9 \\ d=9 \end{gathered}`

Step 3

Find the sum of the first 31 terms

`Sum\text{ of terms of an A.p is given as; S}_n=(n)/(2)(2a+(n-1)d)`
`\begin{gathered} n=31 \\ d=9 \\ a_=5 \\ S_(31)=(31)/(2)(2(5)+(31-1)9) \\ \end{gathered}`
`\begin{gathered} S_(31)=(31)/(2)(10+30(9)) \\ S_(31)=(31)/(2)(280)=4340 \end{gathered}`

Answer;

`S_(31)=4340`