Question

the next term of the A.P in 1²,5²,7²,73 is​

Answer 1

The next term of the A.P. in $1^{2},5^{2},7^{2},73,...$ is $97$.

Step-by-step explanation:

Using n-th term formula:

The given Arithmetic Progression is

$\quad 1^{2},5^{2},7^{2},73,...$

i.e., $1,25,49,73,...$

The first term of the A.P. is $a=1$ and the common difference is $d=25-1=49-25=24$

So, the required term (the fifth term of the A.P.) is

$\quad t_{5}=a+(5-1)d$

$\Rightarrow t_{5}=1+4\times 24$

$\Rightarrow t_{5}=1+96$

$\Rightarrow \boxed{\bold{t_{5}=97}}$

Simply adding common difference:

The given Arithmetic Progression is

$\quad 1^{2},5^{2},7^{2},73,...$

i.e., $1,25,49,73,...$

The common difference of the A.P. is $d=25-1=49-25=24$

So, the required next term is

$\quad 73+d=73+24=\bold{97}$

Formula we must know:

If $a$ be the first term and $d$ the common difference of an Arithmetic Progression, then

• nth term, $t_{n}=a+(n-1)d$

• sum of first n terms, $S_{n}=\dfrac{n}{2}[2a+(n-1)d]$

Answer 2

Step-by-step explanation:

1²=1

5²=25

7²=49

73

let's take a=1

d=25-1=24

or

d=49-25=24

a⁵=a+(n-1)d

1+(5-1)24

1+4×24

1+96

a⁵=97