6 The first and the last terms of an AP are 17 and
350, respectively. If the common difference is 9,
then how many terms are there and what is their
sum?
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Step-by-step explanation:
Hi ,
let a and d are first term and common
difference for an AP.
number of terms of AP = n
last term = nth term = l = an
a = 17 , d = 9 ,
l = 350
a + ( n - 1 ) d = 350
17 + ( n - 1 ) 9 = 350
( n - 1 ) 9 = 350 - 17
( n - 1 ) 9 = 333
n - 1 = 333 / 9
n - 1 = 37
n = 37 + 1
n = 38
Therefore ,
number of terms in given AP = n = 38
sum of n terms of AP = Sn
Sn = n /2 ( a + l )
here n= 38
S38 = 38 / 2 [ 17 + 350 ]
= 19 × 367
= 6973
I hope this helps you.
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