Question

Find the sum of first 20 terms of these sequence whose nth term is an=An+B.

Answer 1

The sum of first 20th term of Arithmetic progression is  210 A + 20 B

Step-by-step explanation:

Given as:

The nth term of an A.P = $a_n$ = A n + B

Let The last term = l = $a_n$ = An + B

Let The sum of first 20 terms of the A.P = $S_2_0$

According to question

First term , $a_1$ of the A.P

$a_1$  = A × 1 + B

i.e $a_1$ = A + B

So, The first term = A + B

Again

Last term (l) or the nth term of the A.P

last term = $a_n$ = A n + B

Now,

The sum of n terms of an A.P = $S_n$

Or, $S_n$ = ( $\dfrac{n}{2}$ ) [ first term + last term ]

Or, $S_n$ = ( $\dfrac{n}{2}$ ) [ ( A + B ) + ( A n + B ) ]

Now, The sum of first 20th term = $S_2_0$

i.e  for n = 20  ,

$S_2_0$ = ( $\dfrac{20}{2}$ ) [ ( A + B ) + ( 20 A + B ) ]

or, $S_2_0$ = 10 × ( 21 A + 2 B )

∴   $S_2_0$ = 210 A + 20 B

So, The sum of first 20th term = $S_2_0$ = 210 A + 20 B

Hence,  The sum of first 20th term of Arithmetic progression is                   210 A + 20 B   Answer