Question
Which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference.
$-225,-425,-625,-825, \ldots . .$
$-225,-425,-625,-825, \ldots . .$
✓
Answer
In the given problem, we are given various sequences.
We need to find out that the given sequences are an A.P. of not and then find its common difference (d),
$-225,-425,-625,-825, \ldots . .$
Here, $a_1=-225, a_2=-425, a_3=-625, a_4=-825$
Difference between terms,
$d_1=a_2-a_1=-425-(-225)=-425+225=-200$
$d_2=a_3-a_2=-625-(-425)=-625+425=-200$
$\text { and } d_3=a_4-a_3=-825-(-625)=-825+625=-200$
Hence, common difference is $-200$ then we say sequance in an A.P.
We need to find out that the given sequences are an A.P. of not and then find its common difference (d),
$-225,-425,-625,-825, \ldots . .$
Here, $a_1=-225, a_2=-425, a_3=-625, a_4=-825$
Difference between terms,
$d_1=a_2-a_1=-425-(-225)=-425+225=-200$
$d_2=a_3-a_2=-625-(-425)=-625+425=-200$
$\text { and } d_3=a_4-a_3=-825-(-625)=-825+625=-200$
Hence, common difference is $-200$ then we say sequance in an A.P.
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