Question

Find the sum of the first 16 terms in an arithmetic series where a1 = 2, and the common difference is d=2.A) 306B) 272C) 240D) 360

Answer 1

B)272

Step-by-step explanation

An arithmetic sequence is defined as a series of numbers, in which each term (number) is obtained by adding a fixed number to its preceding term.

`Sum=(n)/(2)\mleft[2a+(n-1)d\mright],`

where 'a' is the first term, 'd' is the common difference between two numbers, and 'n' is the number of terms.so

Step 1

Let

`\begin{gathered} a=2 \\ d=2 \\ n=16 \end{gathered}`

replace,

`\begin{gathered} Sum=(n)/(2)\lbrack2a+(n-1)d\rbrack, \\ Sum=(16)/(2)\lbrack2\cdot2+(16-1)2\rbrack, \\ Sum=8\lbrack4+(15)2\rbrack \\ Sum=8\lbrack4+30\rbrack \\ Sum=8\lbrack34\rbrack \\ Sum=272 \end{gathered}`

therefore, the answer is

B)272

I hope this helps you