Class 10 Math All topics Arithmetic Progressions

Find the first term and the common difference of an AP, if the $3_{rd}$ term is $6$ and the $1_{th}$ term is $34$.

Solution: If a is the first term and d is the common difference, then nth term, $a_{n}=a+(n−1)d$

Since, $a_{3}=6$ & $a_{17}=34$

$∴a+2d=6$ ...(1)

& $a+16d=34$ ...(2)

On subtracting equation (1) from equation (2), we get $14d=28$$⇒$ $d=2$

Substituting the value of d in equation (1), we get $a=2$

& $a+16d=34$ ...(2)

On subtracting equation (1) from equation (2), we get $14d=28$$⇒$ $d=2$

Substituting the value of d in equation (1), we get $a=2$

$∴$ $a=2$ and $d=2$.

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