Question

In an A. P. if a = 2 and t5 = 12 , find t2, t3, t4.​

Answer 1

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

t2 = 4.5

t3 = 5

t4 = 9.5

$\large {\underline{\underline{\red{\sf{Step-By-Step-Explanation :}}}}}$

First Term (a) of A.P is 2

And fifth term (t5) = 12

Now, The formula for finding term is

$\Large \displaystyle \longrightarrow {\star}{\boxed{\blue{\sf{a_{n} \: = \: a \: + \: (n \: - \: 1)d}}}}$

Put Values

$\Large \implies {\sf{a_{5} \: = \: a \: + \: (5 \: - \: 1)d}}$

Put Values

$\rightarrow {\sf{12 \: = \: 2 \: + \: 4(d)}}$

$\rightarrow {\sf{12 \: - \: 2 \: = \: 4d}}$

$\rightarrow {\sf{10 \: = \: 4d}}$

$\displaystyle \rightarrow {\sf{d \: = \: \frac{\cancel{10}}{\cancel{4}}}}$

$\Large \implies {\underline{\boxed{\green{\sf{d \: = \: 2.5}}}}}$

$\rule{200}{2}$

# Term 2

Put Value in formula :

$\rightarrow {\sf{a_{2} \: = \: 2 \: + \: (2 \: - \: 1)2.5}}$

$\rightarrow {\sf{a_{2} \: = \: 2 \: + \: 2.5}}$

$\Large \hookrightarrow {\boxed{\pink{\sf{a_{2} \: = \: 4.5}}}}$

__________________________

# Term 3

$\rightarrow {\sf{a_{3} \: = \: 2 \: + \: (3 \: - \: 1)2.5}}$

$\rightarrow {\sf{a_{3} \: = \: 2 \: + \: 2(2.5)}}$

$\rightarrow {\sf{a_{3} \: = \: 2 \: + \: 5}}$

$\Large \hookrightarrow{\boxed{\pink{\sf{a_{3} \: = \: 7}}}}$

______________________________

# 4 th Term

$\rightarrow {\sf{a_{4} \: = \: 2 \: + \: (4 \: - \: 1)2.5}}$

$\rightarrow {\sf{a_{4} \: = \: 2 \: + \: 3(2.5)}}$

$\rightarrow {\sf{a_{4} \: = \: 2 \: + \: 7.5}}$

$\Large \hookrightarrow {\boxed{\pink{\sf{a_{4} \: = \: 9.5}}}}$