Arithmetic Progression Problem

[z.js]

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)

 

[Tanya Sharma]

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)

You have used formula of the nth term instead of using that of sum of n terms .28 is not the 7th term .Instead it is the sum of first 7 terms .Similarly with 90 being the sum of first 15 terms.

Use S_n = (n/2)[2a+(n-1)d]

 

[z.js]

ahh! I forgot! thanks