Question

pls answer me fast fast!!!!!!!​

Answer 1

Answer:

The answer is in above attachment

Hope it helps you

Step-by-step explanation:

please Mark as brainliest answer

Answer 2

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:a _1 = 4$

and

$\rm :\longmapsto\:a _n = 4a _{n - 1} \: + \: 3 \: \: where \: n > 1 - - - (1)$

$\red{\bf :\longmapsto\:To \: find \: a _2}$

Substituting n = 2 in equation (1), we get

$\rm :\longmapsto\:a _2 = 4a _{2 - 1} \: + \: 3 \:$

$\rm :\longmapsto\:a _2 = 4a _{1} \: + \: 3 \:$

$\rm :\longmapsto\:a _2 = 4 \times 4 \: + \: 3 \:$

$\rm :\longmapsto\:a _2 = 16 \: + \: 3 \:$

$\red{\rm :\longmapsto\:a _2 = 19}$

$\red{\bf :\longmapsto\:To \: find \: a _3}$

Substituting n = 3 in equation (1), we get

$\rm :\longmapsto\:a _3 = 4a _{3 - 1} \: + \: 3 \:$

$\rm :\longmapsto\:a _3 = 4a _{2} \: + \: 3 \:$

$\rm :\longmapsto\:a _3 = 4 \times 19 \: + \: 3 \:$

$\rm :\longmapsto\:a _ 3 = 76 \: + \: 3 \:$

$\red{\rm :\longmapsto\:a _ 3 = 79 \: }$

$\red{\bf :\longmapsto\:To \: find \: a _4}$

Substituting n = 4 in equation (1), we get

$\rm :\longmapsto\:a _4 = 4a _{4 - 1} \: + \: 3 \:$

$\rm :\longmapsto\:a _4 = 4a _{3} \: + \: 3 \:$

$\rm :\longmapsto\:a _4 = 4 \times 79 \: + \: 3 \:$

$\rm :\longmapsto\:a _4 = 316 \: + \: 3 \:$

$\red{\rm :\longmapsto\:a _ 4 = 319 \: }$

$\red{\bf :\longmapsto\:To \: find \: a _5}$

Substituting n = 5 in equation (1), we get

$\rm :\longmapsto\:a _5 = 4a _{5 - 1} \: + \: 3 \:$

$\rm :\longmapsto\:a _5 = 4a _{4} \: + \: 3 \:$

$\rm :\longmapsto\:a _5 = 4 \times 319 \: + \: 3 \:$

$\rm :\longmapsto\:a _5 = 1276 \: + \: 3 \:$

$\red{\rm :\longmapsto\:a _ 5 = 1279 \: }$

Additional Information :-

In an AP series,

$\rm :\longmapsto\:a _n = a + (n - 1)d$

$\rm :\longmapsto\:S_n = \dfrac{n}{2}\bigg(2a + (n - 1)d\bigg)$

$\rm :\longmapsto\:S_n = \dfrac{n}{2}\bigg(a + a _n\bigg)$

In a GP series,

$\rm :\longmapsto\:a _n = {ar}^{n - 1}$

$\rm :\longmapsto\:S_n = \dfrac{a( {r}^{n} - 1)}{r - 1} \: where \: r \: \ne \: 1$

$\rm :\longmapsto\:S_ \infty = \dfrac{a}{1 - r} \: where \: |r| < 1$