Question

5) The first term of an A.p.is 6 and the common
difference is 3 respectively. Find S27.​

Answer 1

Answer:

1215

Step-by-step explanation:

a=6

d=3

SO , put this in

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

    = 27/2(12+26x 3)

     =1215

Answer 2

Answer :

• The sum of 27 terms is 1275.

Explanation :

Given :

• Common difference of the AP = 3
• First term of the AP = 6
• No. of terms of the AP = 27

To find :

• Sum of 27 terms of the AP, S27 = ?

Knowledge required :

• Formula sum of n terms of the AP :

$\boxed{\sf{S_{n} = \dfrac{n}{2}\bigg(2a_{1} + (n - 1)d\bigg)}}$

Where :

• Sn = Sum of n terms of the AP
• n = No. of terms
• a1 = First term
• d = Common Difference

Solution :

By using the formula for sum of n terms of an AP and substituting the values in it, we get :

$:\implies \sf{S_{n} = \dfrac{n}{2}\bigg(2a_{1} + (n - 1)d\bigg)} \\ \\ \\ :\implies \sf{S_{27} = \dfrac{27}{2} \times \bigg(2 \times 6 + (27 - 1) \times 3 \bigg)} \\ \\ \\ :\implies \sf{S_{27} = \dfrac{27}{2} \times \bigg(2 \times 6 + 26 \times 3 \bigg)} \\ \\ \\ :\implies \sf{S_{27} = \dfrac{27}{2} \times \bigg(12 + 26 \times 3 \bigg)} \\ \\ \\:\implies \sf{S_{27} = \dfrac{27}{2} \times \bigg(12 + 78 \bigg)} \\ \\ \\ :\implies \sf{S_{27} = \dfrac{27}{2} \times 90} \\ \\ \\ :\implies \sf{S_{27} = 27 \times 45} \\ \\ \\ :\implies \sf{S_{27} = 1275} \\ \\ \\ \boxed{\therefore\sf{S_{27} = 1275}}$

Hence the sum of 27 terms of the AP is 1275.