Question

the sum of first 14 odd natural numbers​

Answer 1

SOLUTION

TO DETERMINE

The sum of first 14 odd natural numbers

CONCEPT TO BE IMPLEMENTED

Sum of first n terms of an arithmetic progression

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

Where First term = a

Common Difference = d

EVALUATION

The first 14 odd natural numbers are 1 , 3 , 5 , 7 , . . . ( upto 14 terms )

It is an arithmetic progression

First term = a = 1

Common Difference = d = 3 - 1 = 2

Number of terms = 14

Hence the required sum

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

$\displaystyle \sf = \frac{14}{2} \bigg[(2 \times 1) + (14 - 1) \times 2 \bigg]$

$\displaystyle \sf = 7 \times \bigg[2+ (13 \times 2) \bigg]$

$\displaystyle \sf = 7 \times \bigg[2+26 \bigg]$

$\displaystyle \sf = 7 \times 28$

$\displaystyle \bf = 196$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If for an A.P., S15= 147 and s14=123 find t 15

(A) 24 (B) 23 (C) 47 (D) 46

https://brainly.in/question/34324030

2. Insert there arithmetic means between -20 and 4

https://brainly.in/question/29887163