Question

An AP is -35 , - 30 , - 25 ..... , find the 20th

term of this AP , and the number of

Terms required to obtain a sum = 0 .

Answer 1

1) a = -35 ; d = 5

Using, aⁿ = a + (n-1) d

=> 20th term = -35 + (20-1) × 5

= -35 + 19 × 5

= -35 + 95 = 60

Thus 20th term of A.P. is 60.

2)

n = ? ; Sum of n terms = 0 (Given)

Using,

Sum of n terms =

$(\frac{n}{2}) (2a + (n - 1)d) \\ = (\frac{n}{2}) ( 2 \times ( - 35) + (n - 1) \times 5) \\ = (\frac{n}{2})( - 75 + 5n - 5) \\ = (\frac{n}{2})( - 75 + 5n) \\ = \frac{ - 75n}{2} + \frac{5 {n}^{2} }{2} \\ = \frac{ - 75 + 5 {n}^{2} }{2} \\ = > 0 \times 2 = - 75n + 5 {n}^{2} \\ = > 75n - 5 {n}^{2} = 0$

Answer 2

Step-by-step explanation:

we have to find a20 so,

a20=a+19d

a= -35, d= -05

a20=a+19d

a20= -35+19×-05

a20= -35-95

a20= -130