Question

find the sum of first 20 terms of arthmetic series 2+7+12+..... using suitable formula​

Answer 1

Solution

Given :-

• 20 Terms of AP is 2 + 7 + 12 + ...........

Find :-

• Sum of 20 terms of AP

Explanation

Sum of nth terms of AP

★ Sn = n/2 [ 2a + (n-1)d]

Here,

• n = 20 = Number of terms
• a = 2 = First terms
• d = (7-2) = 5 = Common difference

Keep all values

==> S20 = 20/2 [ 2*2 + (20-1)5]

==> S20 = 10 [ 4 + 19 * 5]

==> S20 = 10 * ( 4 + 95)

==> S20 = 10 * 99

==> S20 = 990

____________________

Hence

• Sum of 20 terms will be = 990

_________________

Answer 2

Questions :-

Find the sum of first 20 terms of an arithmetic series 2 , 7 , 12 , . . . . . using a suitable formula

Answer :-

Given :-

AP = 2 , 7 , 12 , . . . . .

Required to find :-

• Sum of the first 20 terms of the sequence

Formula used :-

$\huge{\dagger{\boxed{\mathsf{ {S}_{nth} = \dfrac{n}{2} [ 2a + ( n - 1 ) d ] }}}}$

Solution :-

Given information :-

AP = 2 , 7 , 12 . . . . .

we need to find the sum of first 20 terms .

So,

Consider the given arithmetic series

AP = 2 , 7 , 12 , . . . . . .

Here,

a = 2

d = ( 2nd term - 1st term ) = ( 3rd term - 2nd term )

=> ( 7 - 2 ) = ( 12 - 7 )

=> ( 5 ) = ( 5 )

So,

d = 5

Using the formula ,

$\huge{\dagger{\boxed{\mathsf{ {S}_{nth} = \dfrac{n}{2} [ 2a + ( n - 1 ) d ] }}}}$

Here,

a = first term

d = common difference

n = the term number till which you want to find the sum

So,

Substitute the required values

However,

$\Rightarrow{\sf{ {S}_{nth} = {S}_{20} }}$

$\Rightarrow{\sf{ {S}_{20} = \dfrac{20}{2} [ 2 ( 2 ) + ( 20 - 1 ) 5 ] }}$

$\Rightarrow{\sf{ {S}_{20} = \dfrac{20}{2} [ 2 ( 2 ) + ( 19 ) 5 ]}}$

$\Rightarrow{\sf{ {S}_{20} = \dfrac{20}{2} [ 2 ( 2 ) + 95 ]}}$

$\Rightarrow{\sf{ {S}_{20} = \dfrac{20}{2} [ 4 + 95 ]}}$

$\Rightarrow{\sf{ {S}_{20} = 10 [ 99 ] }}$

$\implies{\sf{ {S}_{20} = \text{990} }}$

Therefore,

Sum of first 20 terms = 990

Additional knowledge :-

1. The simplified form of the above formula is ;

$\Large{\dagger{\boxed{\mathsf{ {S}_{nth} = \dfrac{n}{2} [ First \; term + Last \; term ] }}}}$

2. The formula to find the nth term of any given arithmetic sequence or progession is ;

$\Large{\dagger{\boxed{\tt{ {a}_{nth} = a + ( n - 1 ) d }}}}$

3. These formulae are very applicable while solving these type of questions !