Question

the sum of first 20 terms of an arithmetic sequence is 480. what is the sum of first and 20th term ?​

Answer 1

Let the arithmetic sequence of the nth term be $a_{n}$.

Let's denote the sum of the first 20 terms as $S_{20}$, $a$ and $l$ as first and last term.

$\rightarrow S_{20}=a+(a+d)+...+(l-d)+l$ ...[Eqn. 1]

$\rightarrow S_{20}=l+(l-d)+...+(a+d)+a$ ...[Eqn. 2]

By adding eqn.1 and eqn.2,

$\rightarrow2S_{20}=20(a+l)$

$\rightarrow S_{20}=10(a+l)$

Therefore,

$\rightarrow 10(a+l)=480$

$\rightarrow a+l=48$

The sum of the first and last term is 48.

Answer 2

Question:-

• The sum of first 20 terms of an arithmetic sequence is 480. what is the sum of first and 20th term ?

To Find:-

• Find the sum of first and 20th term.

Solution:-

• Let the first term be ' a '

• Last term be ' l '

$\longrightarrow\sf \: S_{ 20 } = a + ( a + d ) + . . . . + ( l - d ) + l . . . . . . ( 1 )$

$\longrightarrow\sf \: S_{ 20 } = l + ( l - d ) + . . . . + ( a + d ) + a . . . . . . ( 2 )$

Now ,

We have to add equation ( 1 ) and

( 2 ):-

$\longrightarrow\sf \: 2S_{ 20 } = 20( a + l )$

$\longrightarrow\sf \: S_{ 20 } = \dfrac { 20( a + l ) } { 2 }$

$\longrightarrow\sf \: 480 = 10( a + l )$

$\longrightarrow\sf \: a + l = \cancel\dfrac { 480 } { 10 }$

$\longrightarrow\sf \: a + l = 48$

Hence ,

• Sum of first and last term is 48.