Question

the 1st & the last term of an A.P are 17&350 respectively. if the common differences is 9,how many terms are there and what is their sum

Answer 1

Given a = 17,l=350,d=9.

We know that l = a + (n-1) * d

                       350 = 17 + (n-1) * 9

                       333 = 9n - 9

                       342 = 9n

                      n = 38.

Sum = n/2(a + l)
         
         = 38/2 * (17 + 350)

         = 19 * 367

         = 6973.


Hope this helps!

Answer 2

$\bf\huge\boxed{\boxed{\bf\huge\:Hello\:Mate}}}$

$\bf\huge Let\: a\: first\: terms\: and\: CD\: be\: D \:and\: L\: be\: last\: term$

$\bf\huge a = 17 , L = a_{n} = 350 and D = 9$

$\bf\huge According\:to\:the\:Question$

$\bf\huge => a_{n} = l = 350$

$\bf\huge => a + (n - 1)d = 350$

$\bf\huge => 17 + (n - 1)9 = 350$

$\bf\huge => 9(n - 1) => 350 - 17 = 333$

$\bf\huge => n - 1 = \frac{333}{9} = 37$

$\bf\huge => n = 37 + 1 = 38$

$\bf\huge Substitute\:a = 17 , l = 350 \:and\: n = 38$

$\bf\huge S_{n} = \frac{N}{n}(a + l)$

$\bf\huge S_{38} = \frac{38}{2}(17 + 350)$

$\bf\huge = 19\times 367$

$\bf\huge = 6973$

$\bf\huge\boxed{\boxed{\:Regards=\:Yash\:Raj}}}$