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z.js

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## Homework Statement

If the sum of the first 7 terms of an arithmetic progression is 28 and the sum of the first 15 terms is 90, find the sum of n terms.

## Homework Equations

S

_{n}= 0.5n[2a+(n-1)d]

a is the first term and d is the common difference. n is the number of terms.

n

^{th}term = a + (n-1)d

## The Attempt at a Solution

(here goes )

(1)...a + 6d = 28

(2)...a + 14d = 90

(2)-(1)...8d = 62

...d = 7.75 (ok )

(1)...a + 6(7.75) = 28

.....a = -18.5 (yea! )

(drumrollllllllllll)

S

_{n}= 0.5n(-37 + (n-1)7.75)

= -18.5n +n(n-1)3.875

= n[3.875(n-1) - 18.5]

... now what? the answer was

^{n}/

_{4}(n + 9)