The sum of first n terms of A.P. is 7n2
- 4n. Find the first term, sum of first two terms,
second term. Also find the 20th and nth term of the A.P.
Answers
Step-by-step explanation:
Given:-
The sum of first n terms of A.P. is 7n^2- 4n.
To find:-
Find the following:
1) first term
2) sum of first two terms.
3) Second term
4) find the 20th term
5)Find nth term of the A.P.
Answer:-
Given that
Sum of first n terms of an AP = 7n^2-4n
=> Sn = 7n^2-4n
Put n = 1 then
=>S1 = 7(1)^2-4(1)
=> S1 = 7(1)-4
=> S1 = 7-4
=> S1 = 3
=> t1 = 3
First term = 3
Put n = 2 then
=> S2 = 7(2)^2-4(2)
=> S2 = 7(4)-8
=> S2 = 28-8
=> S2 = 20
Sum of first two terms = 20
=> t1 + t2 = 20
=> 3 + t2 = 20
=> t2 = 20-3
=> t2 = 17
Second term = 17
Common difference (d) = t2 - t1
=> d = 17 - 3
=> d = 14
Common difference = 14
We know that
nth term of an AP is tn = t1 + (n-1)d
20th term = t20
=> t20 = t1 + (20-1)d
=> t20 = t1 + 19 d
=> t20 = 3+ 19×14
=> t20 = 3+266
=> t20 = 269
20th term = 269
nth term = tn
=> tn = t1 + (n-1)d
=>tn = 3+(n-1)(14)
=> tn = 3+14n-14
=> tn = 14n-11
nth term = 14n-11
Answer:-
1) First term of the AP = 3
2) Sum of first two terms of the AP = 20
3) Second term of the AP = 17
4) 20th term of the AP = 269
5) nth term of the AP = 14n -11
Used formulae:-
- nth term of an AP is tn = t1 + (n-1)d
- t1 = First term
- d = Common difference
- n=number of terms