Question

if the first term of the Ap is 1 and common difference is 4 ,then which term of the Ap is 77​

Answer 1

Answer :

• 20th term of the A.P. is 77.

Given :

• First term (a) = 1.
• Common difference (d) = 4.

To Find :

• Which term of the A.P. is 77.

Solution :

We have,

• a = 1

• d = 4

• aₙ = 77

• n = ?

We have to find the n.

We know that,

★ aₙ = a + (n - 1)d

Now, substitute all the given values in the formula.

=> 77 = 1 + (n - 1)(4)

=> 77 = 1 + 4n - 4

=> 77 = 4n - 3

=> 77 + 3 = 4n

=> 80 = 4n

=> 80/4 = n

=> 20 = n

=> n = 20

Hence,

20th term of the A.P. is 77.

Verification :

Now we have,

• a = 1

• d = 4

• aₙ = 77

• n = 20

Substitute all the values in the formula.

Formula : aₙ = a + (n - 1)d

=> 77 = 1 + (20 - 1)(4)

=> 77 = 1 + (19)(4)

=> 77 = 1 + 76

=> 77 = 77

L.H.S. = R.H.S.

Hence Verified.

Answer 2

Given:-

• First term of the A.P is 1 and common difference is 4.

To Find:-

• 77 is which term of the given A.P.

Formula Used:-

• ${\boxed{\bf{a_n=a+(n-1)d}}}$

Solution:-

Using, $\bf a_n=a+(n-1)d$

Here,

• $\bf a_n = 77$

• a = 1

• d = 4

Putting Values,

$\sf :\implies\:77=1+(n-1)4$

$\sf :\implies\:77=1+4n-4$

$\sf :\implies\:77=4n-3$

$\sf :\implies\:4n=77+3$

$\sf :\implies\:n=\dfrac{80}{4}$

$\bf :\implies\:n=20$

Hence, 77 is the 20th term of the given A.P.

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More Formulas related to A.P:-

• $\bf S_n=\dfrac{n}{2}[2a+(n-1)d]$

• $\bf S_n=\dfrac{n}{2}[a+a_n]$

• $\bf S_n=\dfrac{n}{2}[a+l]$

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