Question

If the sum of the first n terms of an A.P. is (1/2)[3n^2 + 7n], then find its nth term. Hence write its 20th term.

Answer 1

Answer:

The nth term is 2 + 3n and 20th term is 62 .

Step-by-step explanation:

GIVEN :

Sn = ½ (3n² + 7n)

First term, a = S1 = ½ [3(1)² + 7(1)]      [n = 1]

S1 = ½ [3 + 7]  

S1= 10/2  

S1= 5

 

S2 = ½ [3(2)² + 7(2)]          [n = 2]

S2 = ½ [3 × 4 + 14]

S2 = ½ [12 + 14]

S2 = ½ × 26

S2 = 13

nth term of the A.P., an = Sn – S(n – 1)

a2 = S2 - S1

a2 = 13 - 5  

a2 = 8

Common difference ,d = a2 - a1  

d = 8 - 5  

d = 3

By using the formula ,nth term , an = a + (n - 1)d

an = 5 + (n - 1) 3

an = 5 + 3n - 3

an = 2 + 3n  

For 20th term :  

an = 2 + 3n  

a20 = 2 + 3 × 20

a20 = 2 + 60

a20 = 62  

20th term = 62  

Hence, the nth term is 2 + 3n and 20th term is 62 .

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