Question

If 12th term of an AP is 213 and the sum of its four term is 24bthen what is the sum of its 10th term?

Answer 1

Answer:

713.4

Step-by-step explanation:

as given

12th term= 213

⇒a+11d=213       --------1

and

sum of 4 terms =24

⇒$\frac{n}{2}[{2a+(n-1)*d}]=24\\\\\frac{4}{2}[2a+(4-1)*d]=24\\\\2[2a+3d]=24\\\\2a+3d=12$   ----------2

by solving equation 1 and 2

a= -26.67

d=21.78

so sum of 10 terms=

 $\frac{10}{2}[2*(-26.67)+9*21.78]\\\\=5[-53.34+196.02]\\\\=5*142.68\\\\=713.4$

Answer 2

Given : 12th term of an AP is 213 and the sum of its four term is 24

To Find : what is the sum of its first 10 terms

Solution:

aₙ = a + (n-1)d

Sₙ = (n/2)(2a + (n-1)d)

12th term of an AP is 213

=> a + 11d  = 213

sum of its four term is 24

(4/2)(2a + 3d)  = 24

=> 2a  + 3d  = 12

a + 11d  = 213 => 2a + 22d = 426

2a + 3d = 12

=> 19d  = 414

=> d = 414/19

a + 11d  = 213

=> a = 213 - 11d

=> a = 213 -  11 * 414/19

=> a =  -507/19

Sum of 10th terms =  (10/2)(2a + 9d)

= 5(2( -507/19) + 9(414/19))

=(5/19)2712

= 13560/19

=713.684

sum of its first 10 terms = 13560/19 =713.684

Learn More:

If the sum of first 8 and 9 terms of na a.P. Are 64 and 361. Find ...

https://brainly.in/question/7677516

Find 5number in a AP whose sum is 25and the sum of square is 135 ...

https://brainly.in/question/8196345

If the sum of first 100 terms of an AP is -1 and the sum of the even ...

https://brainly.in/question/15158022