Class 10 Math All topics Arithmetic Progressions

Find the common difference of am AP: $−225,−425,−625,−825,.....$

Solution: _{}^{}

_{}^{}with first term $a_{1}=−225$ and

Given sequence is,

$−225,−425,−625,−825,...…$

first term of this A.P is $a_{1}=−225$

second term of this A.P is $a_{2}=−425$_{}^{}

third term of this A.P is $a_{3}=−625$

fourth term of this A.P is $a_{4}=−825$_{}^{}

the condition for an sequence to be an A.P is their must be a common difference $(i.e.,d=a_{n+1}−a_{n})$

putting n=1 in above equation

$d=a_{2}−a_{1}=(−425)−(−225)=−200$

putting n=2 in above equation

$d=a_{3}−a_{2}=(−625)−(−425)=−200$

putting n=3 in above equation

$d=a_{4}−a_{3}=(−825)−(−625)=−200$

as we can see we get a common difference $d=−200$ for this sequence

hence this sequence forms an A.P

common difference $d=−200$

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