Question

The nth term of an A.P. -3,-7,-11,-15,.............. is *
1-4n
4n+1
3n-1
none of these

Answer 1

Answer:-

The Required Answer Is Option 1) 1 - 4n.

Explanation:-

Given:-

• An AP -3, -7, -11, -15, ..................n

To Find:-

• The nth term.

Formula Used:-

$\\ \large\bf\longrightarrow a_n = a + (n-1)d.$

Where,

• $\tt a_n$ = n th term.

• a = First term.

• n = Number of terms.

• d = Common Difference.

So Here,

• a = -3.

• d = -7 - (-3) = -4.

Now,

By putting the above values in the formula we get:-

$\\ \tt\mapsto a_n = a + (n - 1)d.$

$\\ \tt\mapsto a_n = ( - 3) + (n - 1)( - 4). \\ \rm \: by \: \: putti ng \: \: values.$

$\\ \tt\mapsto a_n = - 3 + ( - 4n) + 4. \\ \rm by \: \: op en in g \: \: brackets.$

$\\ \tt\mapsto a_n = - 3 + 4 - 4n.$

$\\ \large \red{\mapsto \boxed{ \blue{ \bf a_n = 1 - 4n.}}}$

Therefore The Sum of n th Terms is 1 - 4n.

Answer 2

$\rm{\blue{\underline{\underline{\bold{Answer:-}}}}}$

$\sf{\pink{\therefore 1 - 4n }}$

${\orange{\underline{\underline{\bold{Formula\: Used:-}}}}}$

$\dagger\large{\boxed{\sf{{a}_{n} = a + (n - 1)d}}}$

$\bf{where:-}$

$\tt{\quad \quad \bullet {a}_{n} \: is\: the\: nth\: term \:of \:A.P.}$

$\tt{\quad \quad \bullet a\: is \:the \:first\: term \:of\: A.P.}$

$\tt{\quad \quad \bullet d \:is \:the\: common\: difference}$

$\tt{\quad \quad \bullet n\: is\: the \:number\: of \:terms}$

$\rm{\red{\underline{\underline{\bold{Explanation:-}}}}}$

$\underline{\bf{Here;}}$

$\tt{\quad \quad \bullet a = -3}$

$\tt{\quad \quad \bullet d = (-7) - (-3)}$

$\mapsto\tt{d = -4}$

$\bf{\underline{Using \:the\: formula:-}}$

$\sf{{a}_{n} = a + (n - 1)d}$ $\hookrightarrow\sf{{a}_{n} = -3 + (n - 1)(-4)}$

$\hookrightarrow\sf{{a}_{n} = -3 + (-4n) + 4}$

$\hookrightarrow \sf{\underline{\underline{{a}_{n} = 1 - 4n}}}$

$\red{\large{\underline{\boxed{\bf{Ans. = 1 - 4n}}}}}$