Posted by **simranpreet** on Monday, December 3, 2012 at 6:43am.

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.

- maths -
**Praphul**, Monday, December 3, 2012 at 7:47am
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

- maths -
**Reiny**, Monday, December 3, 2012 at 9:15am
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

## Answer this Question

## Related Questions

- Mathematics - The sum of the 1st and 2nd terms of an AP is 4 and the 10th term ...
- maths - the sum of the 4th and 6th terms of an A.P is 42. the sum of the 3rd and...
- 10th math - The sum of the 4th and 8th terms of an AP is 24 and the sum of the ...
- Math - 1) If the sum of the first n terms of a series is Sn where Sn=2nē-n, (a)...
- math - 1) If the sum of the first n terms of a series is Sn where Sn=2nē-n, (a)...
- Geometric - 1) The sum of last three terms of GP having n terms is 1024 time the...
- Math - Sum of4th and the 6th terms of an a,p is 42 . While the sum of the 3rd ...
- maths - the sum of the first two terms of a GP is 28,but the sum of the third ...
- Math *URGENT - Please give the answers and solutions for each. 1.If the second ...
- Further mathematics - An exponential sequence (GP)of positive terms and a linear...