Question

if ratio of the 11 th of an AP to its 18 th term is 2:3 find the ratio of the first 5 term of its first 10 terms​

Answer 1

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Answer 2

Step-by-step explanation:

Given 11

th

term of an A.P=T

11

=a+10d

and 18

th

term of an A.P=T

18

=a+17d

Ratio=

a+17d

a+10d

=

3

2

⇒3(a+10d)=2(a+17d)

⇒3a+30d=2a+34d

⇒3a−2a=34d−30d=4d

∴a=4d

We have Sum of n terms of an A.P=S

n

=

2

n

(2a+(n−1)d)

Again

S

10

S

5

=

2

10

(2×4d+(10−1)d)

2

5

(2×4d+(5−1)d)

=

10(8d+9d)

5(8d+4d)

=

10×17d

5×12d

=

17

6

Thus, the ratio is 6:17