Question

The sum of 15 terms of a.p. 3,6,9,…

Answer 1

Answer:

The sum of 15 terms of the given A.P is 360.

Step-by-step explanation:

Given :

A.P : 3 , 6 , 9 , ...

To find :

the sum of 15 terms

Solution :

Sum of first n terms of an A.P is given by

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

where

a is the first term

d is the common difference (which is the difference between a term and it's preceding term)

For the given A.P.,

• a = 3

• d = 6 - 3 = 3

Substituting the values,

$\sf S_{15}=\dfrac{15}{2}[2(3)+(15-1)(3)] \\\\ \sf S_{15}=\dfrac{15}{2}[6+14(3)] \\\\ \sf S_{15}=\dfrac{15}{2}[6+42] \\\\ \sf S_{15}=\dfrac{15}{2}[48] \\\\ \sf S_{15}=15 \times 24 \\\\ \underline{\bf S_{15}=360}$

Therefore, the sum of 15 terms of the given A.P is 360.

Answer 2

The sum of 15 terms of AP 3,6,9,.. is 45

Step-by-step explanation:

• An arithmetic progression, also known as an arithmetic sequence, is a set of numbers in which the difference between successive terms remains constant.

Formula: $a = a_1 + (n-1)d$  

• Where;  

$a_n$ = nth term in the sequence

$a_1$ = first term in the sequence

d = common difference between two terms

For 3,6,9; $a_1$ = 3, d: 6-3 = 3

• Therefore, according to the formula, the 15th term would be:

$A_{15} = a_1 + 14d$

$=$ $3 + (14\times3)$

$=$ $3 + 42$  

$=$ $45$

Hence, the answer would be 45.