find the sum of 20 term of an ap which d = 5 and the 11 th term is 55 total sum
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Step-by-step explanation:
Given:-
d=5
11th term=55
To find:-
Find the sum of 20 terms ?
Solution :-
Common difference of an AP=(d)=5
11 th term (t 11)= 55
we know that tn=a+(n-1)d
=>t 11=a + (11-1) (5)
=>55= a+10(5)
=>55=a+ 50
=>a=55-50
=>a=5
First term (a)=5
we know that Sn =(n/2)[2a+(n-1)d]
we have ,n=20
=>S20 = (20/2)[2(5)+(20-1)(5)]
=>S20 = 10[10+19(5)]
=>S20= 10[10+95]
=>S20=10(105)
=>S20=1050
Therefore,S20=1050
Answer:-
The Sum of 20 terms of the given AP =1050
Used formulae:-
If the first term "a" , Common difference "d" and number of terms "n" of an AP then
General or nth term =tn=a+(n-1)d
Sum of n terms =Sn=(n/2)[2a+(n-1)d]
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