# arithmetic sequence

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#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
0
16 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

-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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