# maths

the sum of 3rd and 5th terms of an a.p is 38 and sum of 7th and 10th terms of an a.p is 83,find the a.p.

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1. We have the formula a+(n-1)d=nth term
Where a is the 1st term ,d is the difference and n is the nth term
So1st term= a
2nd term= (a+1)d
3rd term= (a+2)d
5th term=(a+4)d
In the same way 7th term=(a+6)d
10th term=(a+9)d
Subtracting, 9d= 45 which makes d=5

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2. a+2d + a+4d=38 -->2a + 6d = 38
a+6d + a+9d = 83 --> 2a + 15d = 83

subtract them:
9d = 45
d=5

back in 2a+6d = 38
2a+30=38
a=4

the sequence is:

4 9 14 19 24 ...

BTW, the definitions used by Praphul are not correct.
e.g. he said:
5th term is (a+4)d
that should have been a + 4d, the brackets there are critical

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