Class 11

Math

Algebra

Sequences and Series

If the sum of the first $_{′}n_{′}$ terms of an $AP$ is $4n−n_{2}$. What is the sum of first two terms? Find the $3_{rd}$ and the $10_{th}$ terms.

**Solution: **$S_{n}=4n−n_{2}put,n=1S_{1}=4(1)−(1)_{2}S_{1}=4−1=3then,a=3n=2S_{2}=4(2)−(2)_{2}S_{2}=8−4=4S_{2}=4first+sec ond=43+a_{2}=4a_{2}=4−3=1findcommondifference(d)=a_{2}−aa_{n}=a+(n−1)d3rdterm=a_{3}=a+2d=3+2(−2)=3−4=−110thterma_{10}=a+9d=3−+9(−2=3−18 )=−15 $