Question

Given the first term and common difference, find the first four terms and the formula.

Answer 1

The expression for n terms is:

`\begin{gathered} a_n=a_1+(n-1)d \\ \text{where, a}_n=n^(th)term,a_1=\text{ first terms, d = difference} \end{gathered}`

9) first term a1=25, Difference d = 6

For second term put n = 2

`\begin{gathered} a_n=a_1+(n-1)d \\ a_2=a_1+(2-1)d \\ a_2=25+(1)6 \\ a_2=31 \end{gathered}`

for third term: put n =3

`\begin{gathered} a_n=a_1+(n-1)d \\ a_3=a_1+(3-1)d \\ a_3=25+(2)6 \\ a_3=25+12 \\ a_3=37 \end{gathered}`

for fourth term:

Put n =4

`\begin{gathered} a_n=a_1+(n-1)d \\ a_4=a_1+(4-1)d \\ a_4=25_{}+(3)6 \\ a_4=25+18 \\ a_4=43 \end{gathered}`

So, we get:

`\begin{gathered} a_1=25 \\ a_2=31 \\ a_3=37 \\ a_4=43 \end{gathered}`

Thus, First term = 25, Second term = 31, Third term=37, Fourth term = 43

Answer: First term = 25, Second term = 31, Third term=37, Fourth term = 43