The sum of n terms of two arithmetic progressions are in the ratio (3n+8): (7n + 12). Find the ratio of their 10th terms.
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Given that,
- The sum of n terms of two arithmetic progressions are in the ratio (3n+8): (7n + 12).
Let assume that
- First term of first AP is a
- Common difference of first AP is d
- First term of second AP is A
- Common difference of second AP is D
So, According to statement,
Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,
↝ Sum of n terms of an arithmetic sequence is,
Wʜᴇʀᴇ,
- Sₙ is the sum of n terms of AP.
- a is the first term of the sequence.
- n is the no. of terms.
- d is the common difference.
So,
Now, we have to find the ratio of 10th term of two series.
Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,
↝ nᵗʰ term of an arithmetic sequence is,
Wʜᴇʀᴇ,
- aₙ is the nᵗʰ term.
- a is the first term of the sequence.
- n is the no. of terms.
- d is the common difference.
Tʜᴜs,
Now, From equation (1), we have
Put n = 19, we get
From equation (2) and (3), we get
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