Question

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

Answer 1

Given:-

• An A.P = 3, 8, 13, . . . .

To Find:-

• Sum of first 20 terms of an A.P.

Formula Used:-

• ${\boxed{\bf{S_n = \dfrac{n}{2}[2a+(n-1)d]}}}$

Here,

• $\bf S_n$ = Sum of n terms

• a = First term of the A.P

• d = Common Difference

• n = No. of terms in an A.P

Solution:-

Using Formula,

$\bf :\implies\:S_n = \dfrac{n}{2}[2a+(n-1)d]$

Here,

• a = 3

• d = 8 - 3 = 5

• n = 20

Putting values,

$\sf :\implies\:S_{20} = \dfrac{20}{2}[2\times3+(20-1)5]$

$\sf :\implies\:S_{20} = 10[6+19\times5]$

$\sf :\implies\:S_{20} = 10[6+95]$

$\sf :\implies\:S_{20} = 10\times101$

$\bf :\implies\:S_{20} = 1,010$

Hence, The Sum of first 20 terms on given A.P is 1,010.

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