Posted by **Anonymous** on Sunday, February 21, 2010 at 4:42am.

Each term of a progression is determined by adding 0.5 to the preceding term. the sum of the first 25 terms of the progression equals the square of the 25th term. calculate the possible value(s) of the first term

- arithmetic -
**Reiny**, Sunday, February 21, 2010 at 7:36am
As usual, let the first term be a, and we know d = .5

S_{25} = 25/2[2a + 24(.5)] = 25a + 150

T_{25} = a + 24d = a + 12

given: S_{25} = (T_{25})^2

25a + 150 = (a+12)^2

a^2 + 24a + 144 = 25a + 150

a^2 - a - 6 = 0

(a-3)(a+2) = 0

a = 3 or a = -2

## Answer this Question

## Related Questions

- Maths - 1..The first 2 terms of a geometric progression are the same as the ...
- maths - 1) The first term of arithmetic progression is -20 and the sum of it's ...
- c$s college - the first term of an arithmetic progression is 3 and the fifth ...
- maths - the sum of first 8 terms of an arithmetic progression is 156.the ratio ...
- math - The first, the third and the seventh terms of an increasing arithmetic ...
- GP Caluculus - The third term of a geometric progression is 16. The sum of the ...
- GP Caluculus - The third term of a geometric progression is 16. The sum of the ...
- GP Caluculus - The third term of a geometric progression is 16. The sum of the ...
- Maths - Arithmetic Progression - The fourth term of an AP is 8 and the sum of ...
- Arithmetic Progressions - The second term of an arithmetic progression I four ...

More Related Questions