The first term and the last term of an AP are 17 and 350 respectively....

iarc6io

iarc6io

Answered

2022-07-19

The first term and the last term 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 & Explanation

Izabelle Frost

Izabelle Frost

Expert

2022-07-20Added 13 answers

Step 1
Given
First term of A.P ( a 1 ) = 17
Last term of A.P ( a n ) = 350
Common defference ( d ) = 9
Step 2
finding the number of terms and their sum
a n = 350
a 1 + ( 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
= 37 + 1
= 37 + 1
there are 38 terns in A.P
WKT
Some to n terns S n = n 2 [ a + 1 ]
= 38 2 [ 17 + 350 ]
= 19 [ 367 ] = 6973
The sum to 38 terms=6973
Glenn Hopkins

Glenn Hopkins

Expert

2022-07-21Added 4 answers

Given:
First term ( a ) = 17
Last term ( l ) = a n = 350
and common difference ( d ) = 9
a n = 350
a + ( n 1 ) d = 350
17 + ( n 1 ) 9 = 350
9 ( n 1 ) = 350 17 = 333
n 1 = 333 9 = 37
n = 38
Now, S n = n 2 ( a + 1 )
= 38 2 ( 17 + 350 )
= 19 × 367 = 6973
Hence, n = 38 & sum of term S n = 6973

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