Question

first term and common difference of an A. p. are 6 and 3 respectively. find S27​

Answer 1

Answer:

S₂₇ = 1215

Step-by-step explanation:

Given :

In an A.P.,

• first term, a = 6

• common difference, d = 3

To find :

the sum of 27 terms, S₂₇ = ?

Solution :

In an A.P., sum of first n terms is given by,

 $\underline{\boxed{\bf S_n=\dfrac{n}{2}[2a+(n-1)d]}}$

where

a denotes first term

d denotes common difference

Put n = 27,

$\tt S_{27} =\dfrac{27}{2}[2(6)+(27-1)(3)] \\\\ \tt S_{27}=\dfrac{27}{2}[12+26(3)] \\\\ \tt S_{27}=\dfrac{27}{2}[12+78] \\\\ \tt S_{27}=\dfrac{27}{2}[90] \\\\ \tt S_{27}=27 \times 45 \\\\ \tt S_{27}=1215$

Therefore, S₂₇ = 1215

______________________

#Know more :

$\bigstar$ Arithmetic Progression is a sequence where each term is obtained by adding a constant number to the previous term.

$\bigstar$ nth term of an A.P. is given by,

  aₙ = a + (n - 1)d

$\bigstar$ General form of A.P. is

  a , a + d , a + 2d , ....

Answer 2

Answer:

Step-by-step explanation:

$\huge\sf\underline\red{answer}$

given,

first term of an A.P(a) = 6

common difference(d) = 3

solution:

$Sn= \frac{n}{2}[2a+(n-1)d]$

$S_{27} = \frac{27}{2}[12+26(3)]$

$S_{27} = \frac{27}{2}[2(6)+(27-1)3]$

$S_{27} = \frac{27}{2}[12+26(3)]$