Question

the first &the last terms of an AP are 17&350 respectively. if the common difference is 9,then find how many terms are there are what is their sum

Answer 1

a = 17 d= 9 an=350 an=a + (n-1)d. 350=17 + (n-1)9. 333/9= n-1. n-1= 37 n=38. so no. of terms is 38 now sum. sn = n/2(a+an) = 38/2( 17+350) sn = 19*367 sn =6973

Answer 2

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

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

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

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

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

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

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

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

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

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

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

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

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

$\bf\huge = 19\times 367$

$\bf\huge = 6973$

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