Question

the sum of n terms is 3n²/2+5n/2. find 50th term​

Answer 1

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Answer 2

$the\ sum \ of 'n' \ terms \ is \ given \ by\\\\ \frac{3n^2}{2} + \frac{5n}{2} = \frac{3n^2+5n}{2}$

on putting n = 1 we will get the sum of first term that will give us first term

i.e, S₁ = a₁ = (3(1)² + 5(1)) /2 = ( 3+5)/2= 4

so, the first term, a of the AP is 4 ( a₁ = 4 )

on putting n = 2 we will get sum of the first term and the second term

i.e, S₂ = a₁ + a₂ = ( 3(2)²+5(2))/2 = 11

a₁ + a₂ = 11

a₂ = 11 - a₁

a₂ = 11 - 4 = 7

so, common difference , d = a₂ - a₁ = 7 - 4 = 3

so, common difference , d = 3

we have to find,

a₅₀ = a + 49 d

a₅₀ = ( 4 ) + 49 ( 3 )

a₅₀ =  151

hence, the 50th term of this AP is 151.