Question

5. The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the
number of terms.​

Answer 1

The answer is attached

Please mark my answer as brainliest

Answer 2

Step-by-step explanation:

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

$\displaystyle \sf \bigstar \: \: 1st \: term \: = \: 5 \: \: \: \: \: \: \\ \\ \displaystyle \sf \bigstar \: common \: diff \: = 3 \\ \\ \displaystyle \sf \bigstar \: a(n) = 80 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\displaystyle \bigstar \: \sf {\underline{using \: formula}}$

$\displaystyle \longrightarrow \: \boxed{ \underline{ \boxed{ \bold{a(n) = a +( n - 1)d}}}}$

${ \sf{ \underline{ \red{ \underline{ \red{Solution}}}} : -}}$

$\displaystyle \tt : \implies \: a(n) = a + (n - 1)d \\ \\ \displaystyle \tt : \implies \: 80 \: = 5 + (n - 1)3 \: \: \\ \\ \displaystyle \tt : \implies80 = 5 + 3n - 3 \: \: \: \: \: \: \: \\ \\ \displaystyle \tt : \implies80 - 2 = 3n \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \tt : \implies78 = 3n \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \tt : \implies \: n \: = 26 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$