An AP consists of 52 terms of which 3rd term is 13 and the last term is 106.Find the 32th term of the AP.
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Answers
Given that,
An AP consists of 52 terms of which 3rd term is 13 and the last term is 106.
Let assume that, first term of an AP is a and common difference of an AP is d.
So, we have
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,
Also,
On Subtracting equation (1) from equation (2), we get
On substituting the value of d in equation (1), we get
Now, Consider
On substituting the values of a and d, we get
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Additional Information :-
↝ 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.
Answer:
Given that,
An AP consists of 52 terms of which 3rd term is 13 and the last term is 106.
Let assume that, first term of an AP is a and common difference of an AP is d.
So, we have
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,
Also,
On Subtracting equation (1) from equation (2), we get
On substituting the value of d in equation (1), we get
Now, Consider
On substituting the values of a and d, we get
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Additional Information :-
↝ 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.