Question

If the sum of the first 2n terms of the AP 2, 5, 8, ... is equal to the sum of the first n terms of A.P. 57, 59, 61, ... then what is the value of n? [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

Given: 2 + 5 + 8 + ... 2n terms = 57 + 59 + 61 + ... n terms

$S_n=\frac{n}{2}[2a+(n-1)d$
$\Rightarrow \frac{2n}{2}\left[2\right(2)+(2n-1\left)3\right]=\frac{n}{2}\left[2\right(57)+(n-1\left)2\right]$
$\Rightarrow n[4+6n-3]=n[57+n-1]$
$\Rightarrow 6n+1=n+56$
$\Rightarrow 5n=55$
$\Rightarrow n=11$