Question

The 1st term and the common difference of an arithmetic progression is 13 and 5 respectively. Find the sum from 6th term to 20 term.

Answer 1

Answer:

1145

Step-by-step explanation:

Given AP, 1st term is 13 and common difference is 5

Sum of terms of 6th to 20th to be found

Find the sum of 20 terms: 20/2*(13*2+19*5)=10*121=1210

Find the sum of 5 terms: 5/2*(13*2+4*5)=65

Subtract sums: 1210-65=1145

1145 is required sum of 6th to 20th terms

Answer 2

Answer:

Sum from 6th term to 20 term is 1095

Step-by-step explanation:

First term=a=13

Common difference =d=5

Sum from 6th term to 20th term.

6th term=a+5d

6th term=13+5(5)

6th term=13+25

6th term=38.

20th term=a+19d

=13+19(5)

=13+95

20th term=108

Arithmetic series from 6th term is 38, 43, 48....

Now,

A=38, aN=108,

aN=A+(n-1)d

108=38+(n-1)5

108-38=(n-1)5

70=(n-1)5

70/5=n-1

14=n-1

n=14+1

n=15

Sn=n/2(A+aN)

=15(38+108)/2

=15(146)/2

=15(73)

=1095.

Sum from 6th term to 20 term is 1095.

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