Question

Find the third term if T(n + 1) = 4T(n) + 1 and T(1) = 5

Answer 1

Answer:

80

Step-by-step explanation:

3rd term

= T(2+1)

= 4T(2)

= 4[ T(1+1)]

= 4[ 4T(1)]

= 4[ 4(5)]

= 4×4×5

= 80

therefore third term = 80

hope this helps you

Answer 2

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ third \ term \ is \ 85.}$

$\sf\orange{\underline{\underline{Given:}}}$

$\sf{\implies{t(n+1)=4t(n)+1}}$

$\sf{\implies{t1=5}}$

$\sf\pink{\underline{\underline{To \ pink:}}}$

$\sf{Third \ term.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{t(n+1)=4t(n)+1}$

$\sf{Let \ n \ be \ 1}$

$\sf{\therefore{t(1+1)=4t1+1}}$

$\sf{But \ t1=5}$

$\sf{\therefore{t2=4(5)+1}}$

$\sf{\therefore{t2=21}}$

$\sf{Now, \ let \ n \ be \ 2}$

$\sf{t(2+1)=4t2+1}$

$\sf{But \ t2=21}$

$\sf{\therefore{t3=4(21)+1}}$

$\sf{t3=85}$

$\sf\purple{\tt{\therefore{The \ third \ term \ is \ 85.}}}$