Find the ratio of the sum of 11 terms of the two arithmetic progressions if the ratio of the sun to n terms of the two progressions is (7n + 4): (6n-5). A] 64/81 B]144/156
C]81/61 D] 151/121 E] None of these
DA
OB
O C
D
E
Clear Response



Answer :

To solve this problem, we need to find the ratio of the sum of 11 terms of two arithmetic progressions (APs), given that the ratio of the sum to [tex]\( n \)[/tex] terms of the two progressions is [tex]\( \frac{7n + 4}{6n - 5} \)[/tex].

Here is the step-by-step solution:

1. Understand the Ratio Given for n Terms:
The ratio of the sum to [tex]\( n \)[/tex] terms of the two arithmetic progressions is given by:
[tex]\[ \text{Ratio} = \frac{7n + 4}{6n - 5} \][/tex]

2. Substitute [tex]\( n = 11 \)[/tex]:
We need to find this ratio specifically for [tex]\( n = 11 \)[/tex]:
[tex]\[ \text{Ratio for 11 terms} = \frac{7 \times 11 + 4}{6 \times 11 - 5} \][/tex]

3. Calculate the Numerator:
[tex]\[ 7 \times 11 + 4 = 77 + 4 = 81 \][/tex]

4. Calculate the Denominator:
[tex]\[ 6 \times 11 - 5 = 66 - 5 = 61 \][/tex]

5. Form the Ratio:
[tex]\[ \frac{81}{61} \][/tex]

Hence, the required ratio of the sum of 11 terms of the two arithmetic progressions is [tex]\( \frac{81}{61} \)[/tex].

So, the correct option is:
[tex]\[ \boxed{81/61} \][/tex]

The correct answer is Option C.