Question

Which term of the A.P. 37, 34, 31,…..is 16?

Answer 1

Given :

• A.P. = 37, 34, 31,...

To Find :

• Which term is 16 in given A.P.?

Solution :

$\underline{\sf We \: are \: given \: A.P.} :$

• 37, 34, 31,...

$\underline{\sf Here} :$

• First term, a or a₁ = 37
• Second term, a₂ = 34
• Common difference, d = a₂ - a₁ = 34 - 37 = - 3

$\underline{\sf We \: have \: to \: find \: which\: term\: is \: 16} :$

Let n be the term which is 16.

$\sf : \implies a_{n} = 16$

$\underline{\sf Now,\: we\: have\: a\: formula} :$

$\large \underline{\boxed{\bf a_{n} = a+(n-1)d}}$

$\underline{\sf By \: filling \: values} :$

$\sf : \implies 16 = 37 + (n-1)\times (-3)$

$\sf : \implies 16 = 37 -3n+3$

$\sf : \implies 16 = 40 - 3n$

$\sf : \implies 16 - 40 = - 3n$

$\sf : \implies 16 - 40 = - 3n$

$\sf : \implies - 24 = - 3n$

$\sf : \implies 24 = 3n$

$\sf : \implies \cancel{\dfrac{24}{3}} = n$

$\sf : \implies 8 = n$

$\sf : \implies n = 8$

$\Large \underline{\boxed{\bf n = 8}}$

$\underline{\boxed{\sf Hence, \: 8th\: term\: of\: A.P.\: is\: 16.}}$