posted by simranpreet .
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.
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
Adding ad+2d+ad+ 4d= 38
2ad+ 6d= 38
In the same way 7th term=(a+6)d
Adding these 2ad+15d=83
Subtracting, 9d= 45 which makes d=5
a+2d + a+4d=38 -->2a + 6d = 38
a+6d + a+9d = 83 --> 2a + 15d = 83
9d = 45
back in 2a+6d = 38
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