Posted by **Watermelon** on Thursday, November 24, 2011 at 3:48am.

The sixth term of an Arithmetic Progression is 23 and the sum of the six terms is 78. Find the first term and the common difference.

- AP calculus -
**Steve**, Thursday, November 24, 2011 at 5:44am
a+5d = 23

6/2 * [a + (a+5d)] = 78

a + 5d = 23

6a + 15d = 78

a=3

d=4

sequence: 3 7 11 15 19 23

sum: 78

- AP calculus -
**Watermelon**, Thursday, November 24, 2011 at 7:03am
Given an arithmetic progression -7,-3,1,..., state three consecutive terms in this progression which sum up to 75.

- AP calculus -
**Steve**, Thursday, November 24, 2011 at 7:03pm
The kth term is a+(k-1)d

so you want

3a + (k-1 + k + k+1)d = 75

3(-7) + 3k(4) = 75

12k = 96

k=8

So, the 8th,9th,10th terms are

21,25,29 add up to 75

- AP calculus -
**NCaxUXvPLp**, Monday, December 12, 2011 at 4:34am
I can already tell that's gonna be super hlepufl.

## Answer This Question

## Related Questions

- maths - 1) The first term of arithmetic progression is -20 and the sum of it's ...
- Maths - 1..The first 2 terms of a geometric progression are the same as the ...
- Arithmetic Progressions - The second term of an arithmetic progression I four ...
- Math - The fifth term of an arithmetic progression is 19 and the fourteenth term...
- arithmetic - an arithmetic progression has 20 terms. the sum of all the even ...
- arithmetic - In an arithmetic progression the sum of the first 10 terms is 50 ...
- AP Calculus - The 9th term of an arithmetic progression is 4+5p and the sum of ...
- Advanced Algebra - The arithmetic progression has first term 4 and last term 34...
- Mathematics - The 25 term of an Arithmetic Progression is 7 1/2 and the sum of ...
- math - The first, the third and the seventh terms of an increasing arithmetic ...

More Related Questions