Find the sum of first 20 terms of the sequence whose nth term is $a_n = An + B$.

Given:

nth term of a sequence is given by $a_n = An + B$.

To do:

We have to find the sum of the first 20 terms.

Solution:

Here,

\( a_{n}=An+B \)

Number of terms \( =20 \)

\( a_{1}=a=A(1)+B=A+B \)

\( a_{2}=A(2)+B=2A+B \)

\( \therefore d=a_{2}-a_{1}=2A+B-(A+B)=A \)

We know that,

\( S_{n}=\frac{n}{2}[2 a+(n-1) d] \)

\( S_{20}=\frac{20}{2}[2(A+B)+(20-1) d] \)

\( =10[2 A+2 B+(19) \times A] \)

\( =10[2A+2B+19A]=10[21A+2B] \)

\( =210A+20B \)

The sum of the first 20 terms is $210A+20B$.  

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Updated on: 10-Oct-2022

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