Advertisement Remove all ads

The 13th term of an A.P. is four times its 3rd term. If its 5th term is 16, then find the sum of its first ten terms. - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

The 13th term of an A.P. is four times its 3rd term. If its 5th term is 16, then find the sum of its first ten terms.

Advertisement Remove all ads

Solution

 
 

Let the first term be ‘a’ and the common difference be ‘d’ of the A.P.
t13 = 4t3
⇒ a + 12d = 4(a + 2d)
⇒ a + 12d = 4a + 8d

4d = 3a
⇒ a =4d/3
t5 = 16
⇒ a + 4d = 16

`⇒((4d)/3)+ 4d = 16`

`(4d+12d)/3=16`

`(16d)/3=16`

d=3

`a=(4d)/3=(4(3))/3=4`

`S_n=n/2[2a+(n-1)d]`

`S_10=10/2[2xx4+(10-1)xx3]`

=5[8+27]

=5x35

=175

Sum of the first 10 terms =175.

 

 

 
 
Concept: Arithmetic Progression
  Is there an error in this question or solution?
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×