# maths

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.

1. Praphul

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

2. Reiny

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

## Similar Questions

1. ### 10th math

The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of AP
2. ### Geometric

1) The sum of last three terms of GP having n terms is 1024 time the sume of first 3 terms of GP. If 3rd term is 5. Find the last term. 2) The sum of the first eight terms of a GP is five times the sum of the first four terms. Find …
3. ### maths

the sum of the 4th and 6th terms of an A.P is 42. the sum of the 3rd and 9th terms of the progression is 52. find the first term, the common difference and the sum of the first ten terms of the progression.
4. ### Math

Sum of4th and the 6th terms of an a,p is 42 . While the sum of the 3rd and 9th terms of the same a.p is 52. Find the (a) first term (b)common difference (c) sum of the first ten terms of the progression. Solution
5. ### Mathematics

The sum of the 1st and 2nd terms of an AP is 4 and the 10th term is 19. Find the sum of the 5th and 6th terms
6. ### maths

the sum of the first nine terms of an arithmetic sequence 216. The 1st, 3rd and 7th terms form the first three terms of a geometric sequence therefore find the common difference
7. ### maths

in a GP, the sum of the 3rd and 4th terms is -4/3 and the sum of the 4th and 5th terms is -4/9. Find the 6th term.
8. ### math

In a GP, the sum of the 3rd and 4th terms is -4 /3, and the sum of the 4th and 5th terms is -4 /9. Find the 6th term
9. ### mathematics

The sum of first and the second terms of an ap is 4 and the 10th is 19.find the sum of the 5th and 6th terms.
10. ### maths

The sum of the first two terms of a gp is 28, but the sum of the 3rd and 4th terms is 252. find the 2nd term of the GP if the 7th term is 5103.

More Similar Questions