In an AP tenth term is 21 and the sum of its ten terms is 120. Find it’s twentieth term.
Answers
Step-by-step explanation:
Given :-
In an AP tenth term is 21 and the sum of its ten terms is 120.
To find:-
Find it’s 20th term ?
Solution :-
Let the first term of an AP be a
Let the common difference of the AP be d
We know that
The general term of the AP =
an = a+(n-1)d
Sum of first n terms =
Sn = (n/2)[2a+(n-1)d]
Given that
10th term of the AP = 21
=> a10 = 21
=> a+(10-1)d = 21
=> a+9d = 21 -----(1)
and
Sum of the first 10 terms of the AP = 120
=> S10 = 120
=> (10/2)[2a+(10-1)d] = 120
=> (5)[2a+9d] = 120
=> 2a+9d = 120/5
=> 2a +9d = 24-------(2)
On subtracting (1) from (2)
2a + 9d = 24
a + 9d = 21
(-)
____________
a +0 = 3
____________
a = 3
First term of the AP = 3
Now, on substituting the value of a in (1) then
3 + 9d = 21
=> 9d = 21 - 3
=> 9d = 18
=> d = 18/9
=> d = 2
Common difference = 2
Now,
20th term of the AP
=> a 20
=> a+(20-1)d
=> a+19d
=> 3 +(19)(2)
=> 3 + 38
=> 41
a20 = 41
Answer:-
The 20th term of the given AP is 41
Used formulae:-
- The general term of the AP =
- an = a+(n-1)d
- Sum of first n terms =
- Sn = (n/2)[2a+(n-1)d]
- a = first term
- d = Common difference
- n= number of terms
Answer:
Step-by-step explanation:
