two APs have the same common difference. The difference between their 100th terms is 100,what is the difference between their 1000th terms.
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difference between them will be 100
Step-by-step explanation:
ANSWER
a
n
=a+(n−1)d
100th term will be,
a
100
=a+(100−1)d
a
100
=a+99d
100th term of 1st Ap = a + 99d
2nd AP will be,
b
n
=b
n
+(n−1)d
b
100
=b+99d
a
100
−b
100
=100
(a+99d)−(b+99d)=100
a−b=100...(1)
Difference between 1000th term,
=a
1000
−b
1000
=a+(1000−1)d)−[b+(1000−1)d]
=a−b+999d−999d
=
100
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