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

An=a+(n-1)d( by using this we can find the solution)
Given
An= 350
a=17
d=9
n=¿

so just put the value
350=17+(n-1)9
350-17=9n-9
333=9n-9
333+9=9n
342=9n
342÷9=n
38=n

show the number of term is 38
Sn = n/2(a+an)
sn=38/2(350+17)
Sn=19(367)
Sn=6973

Answer 2

Hello !




First term ( A ) = 17



Common difference ( D ) = 9




Last term ( Tn ) = 350



A + ( N - 1 ) × d = 350




17 + ( n - 1 ) × 9 = 350



17 + 9n - 9 = 350



9n = 350 - 8



n = 342/9



n = 38



Number of terms = 38.




Sn = N/2 × [ 2A + ( n -1 ) × D ]



S38 = 38/2 × [ 2 × 17 + ( 38 - 1 ) × 9 ]





=> 19 ( 34 + 333)




=> 19 × 367



=> 6973.