Question

The sum of first 20 terms of AP 3,7,11,15 using formula

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{\red{Solution}}}}}}$

$\Large{\underline{\mathfrak{\bf{\orange{Given}}}}}$

• Terms of AP 3 , 7 , 11 , 15 ........

$\Large{\underline{\mathfrak{\bf{\orange{Find}}}}}$

• Sum of 20 terms of given AP series

$\Large{\underline{\underline{\mathfrak{\bf{\red{Explanation}}}}}}$

Formula of Sum of Nth terms

$\small\boxed{\underline{\tt{\green{\:S_{n}\:=\:\dfrac{n}{2}\times (2a+(n-1)d)}}}}$

Where,

• n = Number of terms
• a = first terms
• d = common difference

On this series

• n = 20
• a = 3
• d = 4

So, using formula for Sum of 20 terms

$\mapsto\tt{\:S_{20}\:=\:\dfrac{20}{2}\times(2*3+(20-1)*4)} \\ \\ \mapsto\tt{\:S_{20}\:=\:10\times(6+19*4)} \\ \\ \mapsto\tt{\:S_{20}\:=\:10\times(6+76)} \\ \\ \mapsto\tt{\:S_{20}\:=\:10\times82} \\ \\ \mapsto\tt{\orange{\:S_{20}\:=\:820}}$

$\Large{\underline{\underline{\mathfrak{\bf{\red{Hence}}}}}}$

• Sum of 20 terms of give series will be = 820

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Answer 2

Given AP is 3 , 7 , 11 , 15 , .....

First term , a = 3

Common difference , d = 7-3 = 4

Sum of n terms in an AP is ,

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

Now we need to find the sum of 20 terms of an AP.

$\rightarrow \bold{S_{20}=\frac{20}{2}[2(3)+(20-1)4] }\\\\\rightarrow \bold{S_{20}=10[6+76]}\\\\\rightarrow \bold{\bf{\blue{S_{20}=820}}}$

So the sum of first 20 terms of AP 3,7,11,... is 820.