Question

Find the first term of an arithmetic progression, if the $6^{th}$ to $9^{th}$ term of the sequence are shown below.
$...196,210,224,238$

• A. 7
• B. 14
• C. 98
• D. 126
• E. 140

Answer 1

The correct option is D 126

Arithmetic progression of nth term-

$a_n=a_1+(n-1)d$

where $a_n=$nth term

$a_1=$ first term

$n=$ number of term

$d=$ difference between terms

As given $9^{th}$ term is $238$, then first term is

$\Rightarrow a_9=a_1+(9-1)14$

$\Rightarrow 238=a_1+8\times 14$

$\Rightarrow 238=a_1+112$

$\Rightarrow a_1=238-112$

$\Rightarrow a_1=126$