Question

Find the first term and the difference in an arithmetic sequence if the 100th term is 32 and the 200th term is 116.

Answer 1

Given

Arithmetic sequence

100th term is 32 and the 200th term is 116.

Find

a) Difference ,d

b) First term , a

Step-by-step explanation

as we know that the nth term of an arithmrtic sequence is given by

`a_n=a+(n-1)d`

according to the question ,

`\begin{gathered} a_(100)=a+99d=32 \\ a_(200)=a+199d=116 \end{gathered}`

solve these two equation by elimination method .

subtract both equation to eliminate a ,

`\begin{gathered} a+99d-a-199d=32-116 \\ -100d=84 \\ d=-0.84 \end{gathered}`

now put value of d in one of the equation,

`\begin{gathered} a+99(-0.84)=32 \\ a-83.16=32 \\ a=32+83.16 \\ a=115.16 \end{gathered}`

Final Answer

therfore , the difference = -0.84 and first term = 115.16