Question

find the sum of the terms in the arithmetic sequence for the number of term indicated.
1. 6+12+18+24+... 15 terms​

Answer 1

Step-by-step explanation:

a=6

d= 6(12-6)

n=15

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

=15/2(2(6)+(15-1)6)

=7.5(12+84)

720

Answer 2

Sum of 15 term in given AP = 720

Given:

6+12+18+24+... 15 terms​ is a Arithmetic Sequence

To find:

Find the sum of the terms in the given Arithmetic Sequence

Solution:

Given 6+12+18+24+... 15 terms​ is a Arithmetic Sequence

Where first term a = 6

Common difference = 12 - 6 = 6

As we know sum of n terms in AP = $\frac{n}{2} [ 2a+(n-1)d} ]$    

⇒ Sum of 15 terms = $\frac{15}{2} [ 2a+(15-1)d} ]$

=  $7.5 [ 2a+14d} ]$

Substitute a = 6 and d = 6

= 7.5 [ 2(6) +14(6) ] = 7.5 [ 96] = 720

Sum of 15 term in given AP = 720

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