Question

find the 8th term from the end of AP 3,7,11,....99​

Answer 1

Answer:

$\bigstar{\bold{Eighth\:term\:from\:the\:end=71}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• The A.P is 3, 7 , 11 ,.....99

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The eighth term from the end of the A.P

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Here we have to find the eight term from the end of the A.P

→ Reversing the A.P we get,

  99,.....11, 7, 3

→ Now we have to find the 8th term from the first of the A.P

→ First we have to find the common difference (d) of the A.P

→ d = 7 - 11 -4

→ Hence common difference of the A.P is -4.

→ The eigth term of an A.P is given by the formula,

   a₈ = a₁ + 7 d

  where a₁ = 99, d = -4

→ Substituting the datas we get,

  a₈ = 99 + 7 × -4

  a₈ = 99 - 28

  a₈ = 71

→ Hence the eight term from the end of the given A.P is 71

$\boxed{\bold{Eighth\:term\:from\:the\:end=71}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ The common difference of an A.P is the difference between its two consecutive terms.

  d = a₂ - a₁

→ The nth term of an A.P is given by

   $a_n=a_1+(n-1)\times d$

Answer 2

Given ,

The AP is 3 , 7 , 11 , ... 99

First term (a) = 3

Common difference (d) = 4

Last term (l) = 99

We know that , the nth term of an AP from end is given by

$\boxed{ \tt{ a_{n} = l - (n - 1)d }}$

Thus ,

$\tt \implies a_{8} = 99 - (8 - 1)4$

$\tt \implies a_{8} =99 - 7 \times 4$

$\tt \implies a_{8} =99 - 28$

$\tt \implies a_{8} =71$

Therefore , the 8th term of given AP from end is 71

Learn more :

The general formula of an AP -

${ \boxed{ \tt{a_{n} = a + (n - 1)}}}$

The sum of first n terms of an AP -

$\boxed{ \tt{s_{n} = \frac{n}{2} \{ a + a_{n} \}}}$

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