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Series: Arithmetic Progression Formula Manipulation
If the first 40 terms of an arithmetic series with common difference
1
---
3
sum to
20
---
7
 then the first term must be

tickcross


Worked Solution:

The formula for the sum, S of n terms of the arithmetic series starting at a whose terms have a common difference of d is:
S =
n (2 a + (n – 1) d )
---
2
For this arithmetic series, we have
n = 40, d =
1
---
3
 and S =
20
---
7
Rearranging to find a we have:
a =
S
---
n
 –
(n – 1) d
---
2
With the values for this series we have:
a =
20
–--
7
---
40
 –
(40 –1)
1
–--
3
---
2
<=>a =
– 45
---
7

© MEI Produced by Dr Ron Knott, revised 15 May 2007
tom . button [AT] mei . org . uk 		Test reference: SeriesAPFormula.html?ref=3329,qu=a