Question

In an AP first term is 13 and ninth term is 61 then what is the common difference

Answer 1

Given :

• First term = 13
• Ninth term = 61

To find :

Common difference

Formula used :

$\sf \: t_{n} \: = \: a \: + \: ( \: n - 1)d$

Here,

• a = First term
• d = Common diffence
• tₙ = nth term

SOLUTION :

$\sf \implies \: 61 \: = \: 13 \: + \: (9 - 1) \times d \\ \\ \sf \implies \: \: 61 \: - \: 13 \: = \: 8d \\ \\ \sf \implies \: \: 8d = \: 48 \\ \\ \sf \implies \: d \: = \: \dfrac{48}{8} \\ \\ \sf \implies \: d \: = \: \: 6$

ANSWER :

Common difference = 6

[ Verification :

$\sf t_{9} \: = \: 13 + (9 - 1)6 \\ \\ \sf \implies \: t_{9} \: = \:13 + (8 \times 6) \\ \\ \sf \implies \: t_{9} \: = 13 + 48 \\ \\ \sf \implies \: t_{9} \: = 61$

]