Question

FIND THE SUM OF AP 1,4,7,10

Answer 1

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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

Answer 2

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Given AP is 1,4,7,10,.....

In given AP first term a=1, common difference d=3

since , Sn =$\frac{n}{2} [2a + (n - 1)d]$......sum of n terms

put n = 20 for sum of first 20 terms

S20 = = $\frac{20}{2} [2(1) + (20 - 1)3]$

S20 = 10 [2+ 57]

S20 = 590