Question

The Tnth term of A.P is given by -4n+15. Find the sum of 1st 20 term of this A.P

Answer 1

HEYA !

Given that,

$a_{n} = - 4n + 15 \\ \\ \Rightarrow \: \: \: a_1 = - 4(1) + 15 = - 4 + 15\\ \\ \Rightarrow \: \: \: a = 11 \\ \\ \text{and} \\ \\ \Rightarrow \: \: \: a _{20} = - 4(20) + 15 = - 80 + 15 \\ \\ \Rightarrow \: \: \: a _{20} = -65$
Now , We know the formula of the sum of first n terms of AP

$S_ {n} = \frac{n}{2} \: (a + a_{n} ) \\ \\\Rightarrow \: \: \: S_{20} = \frac{20}{2} \: ( 11 + a_{20} ) \\ \\ \Rightarrow \: \: \: S_{20} = 10 \times ( 11 - 65)\\ \\\Rightarrow \: \: \: S_{20} = 10 \times ( - 54) \\ \\\Rightarrow \: \: \: \boxed {S_{20} = - 540} \: \: \: \: \: \: \: \: \: \textbf{Ans.}$

Answer 2

Heya !!!

Tn = -4N+15

T1 = -4 × 1 + 15

=> -4 + 15 = 11

And,

T2 = -4 × 2 + 15

=> -8 + 15 = 7

First term (A) => 11

Common difference (D) = T2-T1 = 7-11 = -4

Sn = N/2 × [ 2A + (N-1) × D ]

S20 = 20/2 × [ 2 × 11 + (20-1) × -4) ]

=> 10 × [ 22 + (-76) ]

=> 10 × ( 22-76)

=> 10 × -54

=> -540 .


Hence,


The sum of First 20 term is -540.

HOPE IT WILL HELP YOU....... :-)