Question

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.​

Answer 1

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