The sum of first 10 terms of an arithmetic sequence is 320 and the sum of first 15 terms is 705 . a) write the algebraic expression of the sum . b) write the algebraic expression of the arithmetic sequence?
Answers
Answered by
1
Answer:
Let say AP is
a , a+ d , a+ 2d , ..............................................., a + (n-1)s
Sum on n terms
= (n/2)(a + a +(n-1)d)
= (n/2)(2a + (n-1)d)
Sum of 10 terms = (10/2)(2a + 9d) = 320
=> 2a + 9d = 64
Sum of 15 Terms = (15/2)(2a + 14d) = 705
=> 2a + 14d = 94
=> 5d = 30
=> d = 6
=> a = 5
AP is
5 , 11 , 16 , ........................
nth Term = 5 + (n-1)6
= 6n - 1
Tn = 6n - 1
Sum = (n/2)(2a + (n-1)d)
= (n/2)(10 + (n-1)6)
= (n/2)(10 + 6n - 6)
= n(3n + 2)
= 3n² + 2n
Sn = 3n² + 2n
Similar questions