Question

A.P . if S5 = 35 and S4 =22 then find the 5th term of an AP​

Answer 1

The answer is 13

The fifth term of the AP is 13


STEP-BY-STEP EXPLANATION :-


$s_5 = 35 \\ \\ s_4 = 22 \\ \\ \\ the \: formula \: to \: be \: used \: is \\ \\ \\ t_n = s_n - s_{(n - 1)} \\ \\ so \\ applying \: the \: formula \\ \\ t_5 = s_5 - s_4 \\ \\ t_5 = 35 - 22 = 13$

Thanks!

Answer 2

Step-by-step explanation:

${S}^{5} = 35$

$= > \frac{n}{2} [2a + (n - 1)d] = 35$

$= > \frac{5}{2} [2a + 4d] = 35$

$= > 2a + 4d = 35 \times \frac{2}{5}$

$= > 2a + 4d = 7 \times 2$

$= > 2a + 4d = 14 \: \: \: \: \: \: \: \: \: \: --------1$

${S}^{4} = 22$

$= > \frac{4}{2} [2a + (4 - 1)d] = 22$

$= > 2[2a + 3d] = 22$

$= > 2a + 3d = 11 \: \: \: \: \: \: \: \: \: \: -------- \: 2$

On subtracting equation 1 and 2, we get

d = 3

Now

On substituting the value of d in equation 1, we get

$= > 2a + 4 \times 3 = 14$

$= > 2a + 12 = 14$

$= > 2a = 2$

$= > a = 1$

$5th\:term = a + 4d$

$= 3 + 4 \times 2$

$= 3 + 8$

$= 11$