Question

find the sum of first 20 terms of an ap in which 11th term is 5 and 13th term is 79 ​

Answer 1

PLS DO LET ME KNOW IF MY ANSWER IS RIGHT

Answer 2

The sum of first 20 terms of an A.P is -270.

Step-by-step explanation:

To find : The sum of first 20 terms of an AP in which 11th term is 5 and 13th term is 79 ?

Solution :

The nth term of an A.P is $a_n=a+(n-1)d$

The 11th term is 5.

i.e. $a+10d=5$ ....(1)

The 13th term is 79.

i.e. $a+12d=79$ ....(2)

Subtract (1) from (2),

$a+12d-a-10d=79-5$

$2d=74$

$d=\frac{74}{2}$

$d=37$

Substitute in (1),

$a+10(37)=5$

$a=5-370$

$a=-365$

The sum of n terms of an A.P is

$S_n=\frac{n}{2}[2a+(n-1)d]$

The sum of first 20 terms of an A.P is

$S_{20}=\frac{20}{2}[2(-365)+(20-1)37]$

$S_{20}=10[-730+703]$

$S_{20}=10[-27]$

$S_{20}=-270$

The sum of first 20 terms of an A.P is -270.

#Learn more

If 5^th and 6^th terms of an A.P are respectively 6 and 5. Find the 11^th term of the A.P

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