One of the most important question from arithmetic progression chapter in which we are to find the sum of first 20 terms whose nth term is (5-6n).
Book – RS Aggarwal, Class 10, chapter 5C, question no 3
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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.
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Given: an=5−6n
Find some of the terms of AP:
Put n=1, we get a1=−1= first term
Put n=2, we get a2=−7= second term
Common difference=d=a2−a1=−7−(−1)=−6
Sum of first n terms:
Sn=n/2[2a+(n−1)d]
=n/2[−2+(n−1)(−6)]
=n(2−3n)
Sum of first 20 terms:
S20=20/2[2(−1)+(20−1)(−6)]
=10[−2−114]
=−1160
Sum of its first 20 terms of AP is −1160.