The 3rd term of an AP is 24 and the 5th term is 36. What is the sum of the first 20 terms?
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Let a1, a2, a3, a4, a5, ..., a20 are terms of an A.P
Given that:
a3 = 24
a5 36
We need to find the sum of the first 20 terms.
First we need to find the value of a1 and the common difference r.
We know that:
a3= a1+ 2r = 24 .............(1)
a5= a1+ 4r = 36 ..............(2)
We will subtract (1) from (2) .
==> 2r = 12 ==> r= 6 ==> a1= 24- 12 = 12
Now we know that the sum of n terms of A.P is given by :
Sn = (n/2)*(2a1+ (n-1)*r )
==> S20 = (20/2) ( 2*12 + 19*6) = 10* 138 = 1380.
Then the sum of the first 20 terms is 1380.
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calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
The nth term of an AP can be written as Tn = a + (n-1)d.
T3 = a + 2d = 24
T5 = a + 4d = 36
T5 – T3 = 2d = 12
=> d = 6
a = 24 – 2d = 12
The sum of the first 20 terms is (T1 + T20)*(20/2)
=> (12 + 12 + 19*6)*10
=> 138*10
=> 1380
The required sum of the first 20 terms is 1380.
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