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Question
Find the sum (−5) + (−8)+ (−11) + ... + (−230) .
Solution
(−5) + (−8)+ (−11) + ... + (−230) .
Common difference of the A.P. (d) = a2 - a1
=-8-(-5)
=-8+5
=-3
So here,
First term (a) = −5
Last term (l) = −230
Common difference (d) = −3
So, here the first step is to find the total number of terms. Let us take the number of terms as n.
Now, as we know,
an = a + (n-1) d
So, for the last term,
- 230 = -5 + ( n-1) (-3)
- 230 = -5-3n + 3
-23 +2 = -3n
`(-228)/(-3) = n`
n = 76
Now, using the formula for the sum of n terms, we get
`S_n = 76/2 [2(-5) + (76-1) (-3)]`
= 38 [-10+(75)(-3)]
=38 (-10-225)
= 38(-235)
= -8930
Therefore, the sum of the A.P is Sn = -8930
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