Question

for an AP if S10=150 & S9=126,find t10 (t10=S10-S9 )

Answer 1

Answer:

$T_{10}=24$

Step-by-step explanation:

It is given that $S_{10}=150$⇒$\frac{10}{2}(2a+9d)=150$ (using $\frac{n}{2}(2a+(n-1)d)=S_{n}$)                                        

⇒$2a+9d=30$                                                              (1)

and $S_{9}=\frac{9}{2}(2a+8d)=126$

⇒$2a+8d=28$                                                              (2)

From equations (1) and (2), we get

$2a+9d-2a-8d=30-28$

⇒$d=2$

Putting the value of =2 in equation (1), we get

$2a+18=30$

$a=6$

Now, $T_{10}=a+(n-1)d$

=$6+(10-1)2$

=$6+18$

=$24$

Thus, $T_{10}=24$

Answer 2

Step-by-step explanation:

A=4 ,N=11 ,d =9-4=5

an= a+(n-1) d

a11=4+(11-1)5=4+10(5)

=4+50 =54