Question

find the sum of first 20terms of the arithmetic progression 3,8,13....​

Answer 1

$\maltese$Given sequence :-

3, 8, 13 . .  . .  

$\maltese$To find :-

Sum of first 20 terms

$\maltese$ Solution :-

As they given the sequence is in A. P we have the formula to find the sum of terms that is

$\purple{\boxed{\sf s_n = \dfrac{n}{2}[2a+(n-1)d] }}$

• s_n = sum of terms
• n = no.of terms
• a = first term
• d = common difference

3 , 8, 13 . .  . .

Here the first term is 3 So,

a= 3

n = 20 {ATQ}

d = 8 -3

d = 5[common difference]

So, substituting the values in formula we get

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

$s_n =\dfrac{20}{2} [ 2(3) +(20-1) 5]$

$s_n = 10[ 6+19(5)]$

$s_n = 10[6+95]$

$s_n = 10(101)$

${\boxed{s_n = 1010}}$

So, sum of 20 terms in the given sequence 3, 8, 13 .  .  . is 1010

$\maltese$ Know more :-

A.P means Arthemetic progression That means it follows a certain pattern that is The given sequence common difference should be same

Examples :-

3, 6 , 9 , 12, 15 . . .

It is a Arthemetic progression beacuse its common difference is same i.e

15 - 12 = 3

12 - 9 = 3

9 - 6 = 3

6 - 3 = 3

If you observe the difference that is 3 ,Since it is in A.P .

3, 6 , 9 , 12, 15 .. . In this progression,

a = 3 [first term]

d = 3 [common difference]

n = nth term

For finding nth term we have formula

an = a+(n-1) d