Question

10th std state board question Algebra question >>
* If the sum of First p terms of an arithmetic progression is 3n+n² then find (1) 1st term and sum of first two terms.(2) find 2nd, 3rd and 15th term.

Answer 1

AP:  we use the formula for the sum of n terms :

1)  S_n = 3 n + n²
     S_1 = 3 + 1 = 4  = first term = a
    
2)  S_2 = sum of first two terms =  3 * 2 + 2² = 10

   Hence, 2nd term is  10 - 4 = 6
   =>  common difference  d = 6 - 4 = 2

S_n = 3 n + n² 
S_n-1 = 3 (n-1) + (n-1)² = 3 n - 3 +  n² - 2 n + 1

n th term = S_n - S_n-1 = 2 n + 2

2nd term =  2 * 2 + 2 = 6
3rd term = 2 *3 + 2 = 8
15 th  term  =  2 * 15 + 2 = 32