Question

(1) The first term of an AP is5 and the common dillerence is 4.complete
the following acivity and find the sum of the 12 tons of the A. p​

Answer 1

Step-by-step explanation:

Given:-

The first term of an AP is 5 and the common dillerence is 4.

To find:-

Complete the following acivity and find the sum of the 12 terms of the A.P.?

Solution:-

First term of an AP = (a) = 5

Common difference (d) = 4

a is the first term and d is the common difference then the general form of an AP is

a, a+d, a+2d, ...

a = 5

a+ d = 5+4 = 9

a+2d = 5+2(4)=5+8= 13

a+3d = 5+3(4)=5+12 = 17

The AP : 5,9,13,17....

The general term of the AP = an = a+(n-1)d

=> an = 5+(n-1)(4)

=> an = 5+4n-4

=> an = 4n+1

nth term of the given AP = 4n+1

Now,

Sum of 12 terms = 5+9+13+17+...+(12 terms)

We know that

Sum of first n terms of an AP =

Sn = (n/2)[2a+(n-1)d]

S 12= (12/2)[2(5)+(12-1)(4)]

=>S 12 = (6)[10+(11)(4)]

=> S 12 = (6)[10+44]

=> S 12 = 6(54)

=> S 12 = 324

(or)

Sn = (n/2)(a+an)

=> S 12 = (12/2)[5+4(12)+1]

=> S 12 = (6)[5+48+1]

=> S 12 = 6(54)

=> S 12 = 324

Answer:-

The AP : 5,9,13,17,...

The sum of first 12 terms = 324

Used formulae:-

• a is the first term and d is the common difference then the general form of an AP is a, a+d, a+2d, ...
• The general term of the AP =
• an = a+(n-1)d
• Sum of first n terms of an AP =
• Sn = (n/2)[2a+(n-1)d]
• Sn = (n/2)(a+an)
• n = number of terms