Question

Question 22
Which term of the AP –2, –7, –12,.. will be –77? Find the sum of this AP upto the term –77.

Answer 1

– 2 , - 7, - 12, ……
Let the nth term of the given AP be – 77.
First term, a = - 2 and common difference, d = - 7 – ( - 2 ) = - 7 + 2 = - 5
nth term of an AP, $T_n$ = a + ( n – 1) d
$\Rightarrow -77=-2+(n-1)(-5)$
$\Rightarrow -75=-(n-1)\times 5$
$\Rightarrow (n-1)=15\Rightarrow n=16$
So, the ${16}^{th}$ term of the given AP will be -77.
Sum of n terms of an AP;
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
So, sum of 16 terms i.e., upto the term – 77;
$i.e.,S_{16}=\frac{16}{2}[2\times (-2)+(n-1\left)\right(-5\left)\right]$
$=8[-4+(16-1\left)\right(-5\left)\right]=8(-4-75)$
$=8\times -79=-632$
Hence, the sum of this AP upto the term – 77 is – 632.