Question

In an A.P Sn = 2604 , d = 5 and, an= 159 and a and n​

Answer 1

Here,

$\bf{}S_n = 2604 \\ \bf d = 5 \\ \bf a_n = 159$

We know,

$S_n = \frac{n}{2} \bigg\{2a + (n - 1)d \bigg\} \\ \\ \huge \: or\\ \\ S_n = \frac{n}{2} \bigg\{a + a + ( n- 1)d\bigg\} \: \: \: \: \: \: \: \cdots(1)$

But,

$\rm{}a_n = a + (n - 1)d \\ \rm{}159 = a + (n - 1)d \: \: \: \: \: \: \: \: \: \: \: \: \: \cdots(a)$

Putting Equation a in Equation (1), we get,

$S_n = \frac{n}{2} \bigg\{a + 159 \bigg\} \\ \\ 2604 = \frac{an}{2} + \frac{159n}{2} \\ \\ 5208 = n(a + 159)$