Find the sum of the arithmetic progression 1 4 7 10
Answers
Answer:
The sum of 1+4+7+10+................to 22 terms of an A.P is 715.
Step-by-step explanation:
The given sequence is 1 + 4 + 7 + 10 ..... uptu 22 terms.
It is given that the given progression is arithmetic progression, so first term should 1 and second term should be 4.
Now,
⇒ First term = 1
⇒ Second term = 4
⇒ Common Difference ( d ) = second term - first term
⇒ d = 4 - 1
⇒ d = 3
From the identities of AP, we know that nth term of the AP is a + ( n - 1 )d , where a is the first term & n is the number of the terms and d is the common difference between the terms.
So,
= > 22th term = 1 + ( 22 - 1 )3
= > 22th term = 1 + ( 21 x 3 )
= > 22th term = 1 + 63
= > 22th term = 64
Identity : , where n is the number of terms & a is the first term and is the last term of the AP.
Now,
Sum of 22 term = ( 22 / 2 ) [ 1st term + 22th term ]
= > Sum of 22 terms = 11 [ 1 + 64 ]
= > Sum of 22 terms = 11 x 65
= > Sum of 22 term = 715
Step-by-step explanation:
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