Two arithmetic progressions have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Answers
Answer:
Two arithmetic progressions have the same common difference.
Let, common difference = d
First term of first A.P. = a
First term of second A.P. = a’
Given that difference between their 100th term is 100
100th term of first A.P., a100 = a + 99d
100th term of second A.P., a’100 = a’ + 99d
Acc. To question,
a100 – a’100 = 100
a + 99d – a’ – 99d = 100
a – a’ = 100 (i)
1000th term of first A.P., a1000 = a + 999d
1000th term of second A.P., a’1000 = a’ + 999d
Acc. To question,
a1000 – a’1000 = a + 999d – a’ – 999d
= a – a’
a1000 – a’1000 = 100 [from (i)]
Hence, difference between 1000th term of two A.P. is 100
Answer:
Two arithmetic progressions have the same common difference.
Let, common difference = d
First term of first A.P. = a
First term of second A.P. = a’
Given that difference between their 100th term is 100
100th term of first A.P., a100 = a + 99d
Step-by-step explanation: