Question

the nth term of A.P is represented by an = 3n + 1. Find the A.P and sum of first 20 terms​

Answer 1

Answer:

see the attached pic for solution.

answer is 650

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The nth term of an AP is represented by$\rm a_{n} = 3n + 1$

$\bf{\underline{\underline\blue{To\: Find:-}}}$

• The sum of first 20 terms of the AP.

$\bf{\underline{\underline\green{Solution:-}}}$

Given:-

$\rm\implies a_{n} = 3n + 1$

First term:-

Substitute n = 1

$\rm a_{1} = 3(1) + 1$

$\rm a = 3 + 1$

$\rm a = 4$

Second term:-

Substitute n = 2

$\rm a_{2} = 3(2) + 1$

$\rm a_{2} = 6 + 1$

$\rm a_{2} = 7$

Now, let us find the common difference (d)

$\rm d = a_{2} - a$

$\rm d = 7 - 5$

$\rm d = 3$

Common difference = 3

First term = 4

Number of terms = 20

As we know that

Sum of n terms is given by the formula:-

$\boxed{\rm S_{n} = \frac{n}{2} \bigg \{2a + (n - 1)d \bigg \} }$

Substituting the values:-

${\rm = \dfrac{20}{2} \bigg \{2 \times 4 + (20- 1)3\bigg \} }$

${\rm = 10\bigg \{8 +(19 \times 3)\bigg \} }$

${\rm = 10(8 +57)}$

${\rm = 10(65)}$

${\rm =650}$

$\underline{\boxed{\purple{\rm\therefore The \:sum\: of \:20 \:terms = 650}}}$