Question

Find auo in the arithmetic sequence: 100, 110, 120, 130, (Use the equation an= a1 + (n - 1)d. Em A B 200 C 190 D

Answer 1

100, 110, 120, 130, (Use the equation an= a1 + (n - 1)d

step 1

Find the common difference d

we have

a1=100

a2=110

a3=120

a4=130

so

a2-a1=110-100=10

a3-a2=120-110=10

a4-a3=130-120=10

the common difference d is equal to 10

d=10

step 2

substitute in teh formua

`\begin{gathered} a_n=a_1+(n-1)\cdot d \\ we\text{ have} \\ a_1=100 \\ d=10 \\ \text{substitute} \\ a_n=100+(n-1)\cdot10 \\ a_n=100+10n-10 \\ a_n=90+10n \end{gathered}`

If you want to calculate the a7 term

then

For n=7

substitute in the formula

`\begin{gathered} a_7=90+10\cdot7 \\ a_7=160 \end{gathered}`