For a finite $A.P.$,the first term is $17$ and the last term is $350$. If the common difference is $9$,find the number of terms in the $A.P.$ and also find their sum.
(N/A) Given: First term $a = 17$,last term $l = a_n = 350$,and common difference $d = 9$.
Using the formula for the $n^{th}$ term: $a_n = a + (n - 1)d$.
Substituting the values: $350 = 17 + (n - 1)9$.
$350 - 17 = (n - 1)9$.
$333 = (n - 1)9$.
$n - 1 = 333 / 9 = 37$.
$n = 37 + 1 = 38$.
Now,to find the sum $S_n$ using the formula $S_n = (n/2)(a + l)$:
$S_{38} = (38 / 2)(17 + 350)$.
$S_{38} = 19 \times 367$.
$S_{38} = 6973$.
Thus,the number of terms is $38$ and the sum is $6973$.
Using the formula for the $n^{th}$ term: $a_n = a + (n - 1)d$.
Substituting the values: $350 = 17 + (n - 1)9$.
$350 - 17 = (n - 1)9$.
$333 = (n - 1)9$.
$n - 1 = 333 / 9 = 37$.
$n = 37 + 1 = 38$.
Now,to find the sum $S_n$ using the formula $S_n = (n/2)(a + l)$:
$S_{38} = (38 / 2)(17 + 350)$.
$S_{38} = 19 \times 367$.
$S_{38} = 6973$.
Thus,the number of terms is $38$ and the sum is $6973$.
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