arithmetic sequence Watch

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salem
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#1
Report Thread starter 15 years ago
#1
Hello !

I have the following questions:

1)The sum of an arithmetic series is 270.The common difference is 1and the the first term is 4.Calculate the number of terms in the series.

2) The first term of an arithmetic series is 16.The 30th term is 100.Calculate S
30.

Best regards,

SALEM
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#2
Report 15 years ago
#2
1) Sum of an AP = 1/2n (2a + (n-1)d)

==> 270 = 1/2n (2x4 + (n-1)x1)

==> 540 = n (8 + n - 1)

==> 540 = n(n + 7)

==> 540 = n^2 + 7n

==> n^2 + 7n - 540 = 0

Using Quadratic Formula

-7 +- sq rt 2209
----------------- = ( -7 + 47 ) / 2 = 40 / 2 = 20
2

So n=20.

There are 20 terms in this sequence


2) Sn = 1/2n (a +l)

Where n= 30, a= 16, l = t(30) = 100

So S(30) = 1/2 (30) (16 + 100)
= 15 x 116
= 1740

S(30) = 1740
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