Question

Find the number of terms of the sequence.
$18,15$${}^{1_{/2}}$, $13,..-49$ ${}^{1_{/2}}$.

Answer 1

$18,{15}_{1/2},13....-{49}_{1/2}$

This sequence forms an A.P within first term a = 18

& the common different d = -2.5

The $n^{th}$ term of A.P is given by (a + (n - 1)d)

$a+(n-1)d=-{49}_{1/2}$

$18+(n-1)(-2.5)=-49.5$

$18+(n-1)(-2.5)-49.5$

$(n-1)(-2.5)=-49.5-18$

$(n-1)(-2.5)=-67.5$

$(n-1)=\frac{-67.5}{-2.5}$

(n-1) = 27

n=28

Hence the number of terms in the sequence is 28 Answer