Question

for the sequence 25,22,19,16... find. A. formula for the nth term B. sum of the first 20 teams

Answer 1

Given:-

$25,22,19,16,\ldots$

To find the nth term and the sum of first 20 terms.

So now we use the formula,

$T_n=a+(n-1)d$

So the value of a is the first term 25 and the value of d is,

$d=22-25=-3$

So the nth term is,

$T_n=25+(n-1)(-3)$

So the sum of terms formula is,

$Sn=\frac{n}{2}\lbrack2a+\mleft(n-1\mright)d\rbrack$

So substituting we get,

$\begin{gathered} Sn=\frac{n}{2}\lbrack2a+(n-1)d\rbrack \\ S_{20}=\frac{20}{2}\lbrack2\times25+(20-1)(-3)\rbrack \\ S_{20}=10\lbrack50+(-3)(19)\rbrack \\ S_{20}=10\lbrack50-57\rbrack \\ S_{20}=10\lbrack-7\rbrack \\ S_{20}=-70 \end{gathered}$

So the sum of terms is -70.