Question

If the sum of the first 13 terms of an ap and the sum of the next 12 terms of the progression are in the ratio of 26:49, then what is the ratio of 13th term to the 7th term of the progression?

Answer 1

By finding a and D u can get s7

Answer 2

Answer:

7:3

Step-by-step explanation:

Given,

The sum of the first 13 terms of an ap and the sum of the next 12 terms of the progression are in the ratio of 26:49

To Find,

The ratio of 13th term to the 7th term of the progression

So,

Sum of n terms =S(n) = n/2( 2a+ (n-1)d)

Let the two APs be:

a', a'+d', a'+2d’,…… a' + (n-1)d'

a”, a”+d”, a”+2d”,….a”+(n-1)d”

Then,

S(13)’ = 13/2 { 2a’+ 12d’}

S(13)”= 13/2 {2a”+12d”}

Also , S(13)’/ S(13)” =( a'+ 6d’)/ (a”+6d”)=7/3 (given)→ equation (1)

But we know that , nth term = a +(n-1)d

Therefore , 7th term= a+6d

Substituting this in equation (1), we get

a(7)’/ a(7)”= 7/3

Hence, ratio of the 7th terms of the given progressions is 7:3.

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