Show thet the followiong sequences is an A.P. Also, find the comm… - Vidyadip

Question

Show thet the followiong sequences is an A.P. Also, find the common difference and write 3 more terms in each case.
$-1,\frac{1}{4},\frac{3}{2},\frac{11}{4},...$

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Answer

$-1,\frac{1}{4},\frac{3}{2},\frac{11}{4},...$
$\text{a}_1=-1,\text{a}_2=\frac{1}{4},\text{a}_3=\frac{3}{2},\text{a}_4=\frac{11}{4}$
$\text{a}_4-\text{a}_3=\text{a}_3-\text{a}_2=\text{a}_2-\text{a}_1=\frac{5}{4}$
$\therefore$ common differnce is $\text{d}=\frac{5}{4}$
$\therefore$ The given sequence is A.P
$\text{a}_5=-1+(5-1)\frac{5}{4}=4$
$\text{a}_6=-1+(6-1)\frac{5}{4}=\frac{21}{4}$
$\text{a}_5=-1+(5-1)\frac{5}{4}=\text{a}_{4}$
$=-1+(7-1)\frac{5}{4}=\frac{26}{4}=\frac{13}{2}$

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