Question

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

Answer 1

1) According to formula for number of terms,

Tn=a+(n-1)d, where Tn=350, a=17, d=9 and n is to be calculated.

Putting these values in the formula we get,

350=17+(n-1)x9
Rearranging, we get,

350-17/9=n-1
37+1=n
So, n=38

2) For sum of the terms, Sn= n/2[2a+(n-1)d]
Putting the values of a, n and d we get,

Sn= 38/2[2x17(38-1)x9]
Sn= 19x[34x37x9]
Sn= 215118 [ANS.]

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Answer 2

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

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

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

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

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

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

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

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

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

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

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

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

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

$\bf\huge = 19\times 367$

$\bf\huge = 6973$

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