Question

the first and last term of AP are 17 and 350 respectively if the common difference is 9 find how many terms are there and what is their sum

Answer 1

a= 17

an = 350

d=9

a+(n-1)d=an

17+(n-1)9=350

17+9n-9=350

9n-9=350-17

9n-9=333

9n=333+9

9n=342

n=342/9

n= 38
38 terms....


sum= n/2[2×a+(n-1)d]

=38/2 [2×17+(38-1)9]

= 19[34+37×9]

= 19[34+333]

= 19[367]

= 6973

sum is 6973....

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Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

a = 17

$\rightarrow{l(Last\; term)\;= a_{n} =350}$

d = 9

★Hence

$\rightarrow{l=a_{n}=350}$

a + (n - 1)d = 350

★Substitute the values :-

17 + (n - 1) × 9 = 350

(n - 1) × 9 = 350 - 17

(n - 1) × 9 = 333

9(n - 1) = 333

${\boxed{\sf\:{(n-1)=\dfrac{333}{9}}}}$

n - 1 = 37

n = 37 + 1

n = 38

★Now sum :-

★Substitute the values

a = 17 , l = 350 and n = 38

${\boxed{\sf\:{S_{n}=\dfrac{n}{2}(a+l)}}}$

${\boxed{\sf\:{S_{38}=\dfrac{38}{2}(17+350)}}}$

= 19 × 367

= 6973

★Therefore

$\fbox{Sum\;is\;6973\;and\;there\;are\;38\;terms}$