Question

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.
please help all questions please help please.

Answer 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
Adding ad+2d+ad+ 4d= 38
2ad+ 6d= 38
In the same way 7th term=(a+6)d
10th term=(a+9)d
Adding these 2ad+15d=83
Subtracting, 9d= 45 which makes d=5

Answer 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