Question

find next four terms of sequence 1/6,1/4,1/3 also find Sn​

Answer 1

this is your answer.

hope it's helpful

please like

Answer 2

Given:-

First three terms of a sequence i.e., $\frac{1}{6},\frac{1}{4},\frac{1}{3}$

To Find:-

Next four terms and sum $S_{n}$

Explanation:-

Since, given sequence is an arithmetic progression.

$\text{Therefore, common difference(d)}=\frac{1}{4}-\frac{1}{6}=\frac{1}{12}$

Now, add $\frac{1}{12}$ in every term to obtain the next term.

$\Rightarrow\text{fourth term, }a_{4}=\frac{1}{3}+\frac{1}{12}=\frac{5}{12}\\\\\text{fifth term, }a_{5}=\frac{5}{12}+\frac{1}{12}=\frac{1}{2}\\\\\text{sixth term, }a_{6}=\frac{1}{2}+\frac{1}{12}=\frac{7}{12}$

$\text{seventh term, }a_{7}=\frac{7}{12}+\frac{1}{12}=\frac{2}{3}$

The general expression to calculate sum in arithmetic progression upto 'n' terms is given by:-

$S_{n}=a_{1}+(n-1)\times d$

$\text{Sum upto n=7 terms, }S_{7}=a_{1}+(7-1)\times d\\\\S_{7}=\frac{1}{6}+6\times\frac{1}{12}=\frac{1}{6}+\frac{1}{2}=\frac{4}{6}=\frac{2}{3}$