Question

Find tn for following AP and then find 30th term of AP 3,8,13,18

Answer 1

$\huge{\mathfrak{\underline{\underline{\red{Answer :-}}}}}$

30th term is 148

$\large{\mathrm{\underline{\gray{Given :-}}}}$

A.P :- 3, 8,13, 18

First term(a) = 3

${\sf{Common \:\: difference(d) \: = \: a_{2} - a_{1}}}$

Common difference = 8 - 3 = 5

$\large{\mathrm{\underline{\gray{To \: Find :-}}}}$

$\bf{T_{30}}$

$\large{\mathrm{\underline{\gray{Solution :-}}}}$

First Method :-

$\bf{T_{30} \: = \: a + 29d}$

__________________[Put Values]

$\bf{T_{30} \: = \: 3 + 29(5)}$

$\bf{T_{30} \: = \: 3 + 145}$

$\bf{T_{30} \: = \: 148}$

Second Method :-

Using Formula

$\huge{\boxed{\boxed{Tn \: = \: a + (n - 1)d}}}$

__________________[Put Values]

$\bf{T_{30} \: = \: 3 + (30 - 1)5}$

$\bf{T_{30} \: = \: 3 + 29(5)}$

$\bf{T_{30} \: = \: 3 + 145}$

$\bf{T_{30} \: = \: 148}$

$\huge{\boxed{\boxed{\blue{T_{30} \: = \: 148}}}}$