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Question
Find the sum of first n terms of an AP whose nth term is (5 - 6n). Hence, find the sum of its first 20 terms.
Solution
Let an be the nth term of the AP.
∴ an = 5-6n
Putting n = 1,we get
First term, a = a1 = 5-6 × 1 = -1
Putting n = 2,we get
a2 = 5-6 × 2 = -7
Let d be the common difference of the AP.
∴ d = a2 - a1 = -7 - (-1) = -7 + 1 =-6
Sum of first n tern of the AP, Sn
`= n/2 [ 2 xx (-1) + (n-1) xx (-6) ] {s_n = n/2 [ 2a +(n-1) d]}`
`=n/2 (-2 - 6n +6)`
=n(2 -3n)
= 2n -3n2
Putting n = 20,we get
` s_20 = 2 xx 20- 3 xx20^2 = 40- 1200 = -1160`
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