Question

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Answer 1

$\huge(\textcolor{red} {Answer : 38 \; terms \; and \; Sum \; 6973})$

$\textit{ Explanation :}$

\textbf{Given,

l ( last term ) = 350

a ( first term ) = 17}

d ( common difference ) = 9

{We know,

no. of terms in an AP = $\frac{last \; term - first \; term}{common \; difference} + 1$}

Substituting the values we get,

no. of terms =$\frac{350 - 17}{9}+1$

= $\bf{37+1}$

n= $\bf{38}$

Sum of an AP = $\frac{n}{2}×(first \; term + last \; term)$

Substituting the values we get,

Sum = $\frac{6973}{1}$

= 6973

Answer 2

❤❤Here is your answer ✌ ✌

$\huge\boxed{\red{\bold{Answer}}}$

$\huge\underline{\green{\bold{Given}}}$
$<b>$
firstl term = a = 17

Last term = tn = 350

Number of term =?

$\huge\underline{\blue{\bold{Now}}}$
$<b>$
tn=a+(n-1)d
350=17+(n-1)9
350-17=(n-1)9
333=9n-9
333+9=9n
342=9n
38=n✔✔

Number of term=38

sum =n/2×(a+l)
➡38/2×(17+350)
➡38/2×367
➡6973
sum of 1st and last term➡6973✔✔