In an A.P., the first term is 7 and the last term is 205. If sum of all numbers in the A.P. is 3604, find the number of terms and common difference
Answers
Sum of AP
Answer: Number of terms in AP are 34 and common difference is 6.
Explanation:
Given that first term of AP that is a = 7
last term of AP that is l = 205
Sum of all numbers = S = 3604
Need to determine number of terms and common difference.
Formula of Sum of AP in terms of first and last term is as Follows
S = n/2 ( a + l ) where n is total number of terms in AP
On substituting given values
3604 = n/2( 7 + 205 )
=> 3604 × 2 = n × 212
⇒ 3604 × 2 / 212 = n
⇒ n = 34
Formula of Sum of AP in terms of first term and common diffrence is as Follows
S = n/2 ( 2a + (n-1)d )
as total number of term is n = 34 , so sum of 34 terms will be same as sm of all numbers in AP that is 3604
⇒ 3604 = 34/2 ( 2 x 7 + (34 - 1 ) d )
⇒ 3604/17 = 14 + 33d
⇒(212 - 14)/33 = d
⇒ d = 6
Hence number of terms in AP are 34 and common difference is 6.