Find the common difference and write the next four terms of the f… - Vidyadip

Question

Find the common difference and write the next four terms of the following arithmetic progressions:
$-1,\frac{1}{4},\frac{3}{2},\ .....$

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Answer

Given arithmetic progression is,
$-1,\frac{1}{4},\frac{3}{2},\ .....$
$\text{a}_1=-1,\text{a}_2=\frac{1}{4},\text{a}_3=\frac{3}{2},\ .....$
Common difference $(d) = a_2 - a_1$
$=\frac{1}{4}-(-1)$
$=\frac{1+4}{4}$
$\text{d}=\frac{5}{4}$
To find next for terms.
$\text{a}_4=\text{a}_3+\text{d}=\frac{3}{2}+\frac{5}{4}=\frac{6+5}{4}=\frac{11}{4}$
$\text{a}_5=\text{a}_4+\text{d}=\frac{11}{4}+\frac{5}{4}=\frac{16}{4}$
$\text{a}_6=\text{a}_5+\text{d}=\frac{16}{4}+\frac{5}{4}=\frac{21}{4}$
$\text{a}_7=\text{a}_6+\text{d}=\frac{21}{4}+\frac{5}{4}=\frac{26}{4}$
$\therefore\ \text{d}=\frac{5}{4},\text{d}_4=\frac{11}{4},\text{a}_5=\frac{16}{4},\text{a}_6=\frac{21}{4},\text{a}_7=\frac{26}{4}.$

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