Question

which term of AP 3,10,17.... will be 84 more than is 13term
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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$\bigstar{\bold{Term\:which\:is\:84\:more\:than\:13th\:term=25}}$

Step-by-step explanation:

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

• The A.P 3, 10, 17........

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

• The term which is 84 more than the 13th term

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

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

➙ d = a₂ - a₁

➙ Substitute the data,

    d = 10 - 3

    d = 7

➙ Hence the common difference of the A.P is 7

➙ Now we have to find the 13th term

➙ The 13 th term of the A.P is given by,

    a₁₃ = a₁ + 12d

➙ Substitute the data,

    a₁₃ = 3 + 12 × 7

    a₁₃ = 3 + 84

    a₁₃ = 87

➙ Hence the 13 th term of the A.P is 87

➙ Now the term which is 84 more than 13th term is

    $a_n$ = 84 + 87 = 171

➙ We have to find which term of the A.P is 171

    $\sf{a_n=a_1+(n-1)\times d}$

➙ Substitute the data,

    171 = 3 + (n - 1) × 7

    171 = 3 + 7n - 7

    171 = 7n - 4

    7n = 175

      n = 175/7

      n = 25

➙ Hence the 25th term of the A.P is 84 more than 13th term

    $\boxed{\bold{Term\:which\:is\:84\:more\:than\:13th\:term=25}}$

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

➙ The nth term of an A.P is given by,

    $\sf{a_n=a_1+(n-1)\times d}$

➙ The common difference of an A.P is given by

    $\sf{d=a_2-a_1}$

    $\sf{d=\dfrac{a_m-a_n}{m-n} }$