Question

For an A, P, $\frac{1}{3},\frac{4}{3},\frac{7}{3},\frac{10}{3}..........,$ Find $T_{{18}^o}$
For an A, P, 3, 9, 15, 21 ............, Find $S_{{10}^o}$

Answer 1

Given A.P.: $\frac{1}{3},\frac{4}{3},\frac{7}{3},\frac{10}{3},..........$
Here, $a=\frac{1}{3}$
And, $d=\frac{4}{3}-\frac{1}{3}=1$
Now, $T_n=a+(n-1)d$
$\therefore T_{18}=\frac{1}{3}+17\left(1\right)=\frac{1}{3}=\frac{11+51}{3}=\frac{52}{3}$
Also, given A. P. : 3, 9, 15, 21, .............
Here, a = 3
And, d = 9 - 3 = 6
Now, $S_n=\frac{n}{2}[2a+(n-1\left)\right]d$
$\therefore S_{10}=\frac{10}{2}\left[2\right(3)+9(6\left)\right]=5[6+54]=5\times 60=300$