Question

25) In an Arithmetic Progression the difference between 18th term and 8th term is 20 and

the first term is 3. Find the sum of first 10 terms​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

120

Step-by-step explanation:

In an Arithmetic Progression the difference between 18th term and 8th term is 20.

$a_{18} -a_{8} =20$

$(a+17d)-(a+7d)=20$                  ($a_{n} =a+(n-1)d$)

$a+17d-a-7d=20$

$17d-7d=20$

$10d=20$

$d=\frac{20}{10}$

$d=2$.

Here is given that first term $a=3$.

And $d=2$.

Sum of first n term of A.P is   $S_{n} =\frac{n}{2}[2a+(n-1)d]$

Therefor sum of first 10 term is  

$S_{10} =\frac{10}{2}[2(3)+(10-1)2]$

$S_{10} =5*[6+(9)2]$

$S_{10} =5*[6+18]$

$S_{10} =5*[24]$

$S_{10} =120$

Therefor sum of first 10 term of A.P is 120.

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