Question

if the 19th term of an A.P is 47, then find the sum of the first 37 terms

Answer 1

Solution:-

Let a be the first term and d be the common difference of the given AP.
So, according to the question.
a₁₉ = 47
⇒ a + 18d = 47 ................(1)
Now, sum of the first n terms of an AP is given by :
Sn = n/2 {2a + (n - 1)d}
= 37/2 {2a + (37 - 1)d}
= 37/2 {2a + 36d}
= 37 {2a + 18d}
Substituting the value of a + 18d = 47 in the above, we get
=37 × 47
1739
So, the sum of the first 37 terms is 1739
Answer.

Answer 2

Answer:

Let a be the first term and d be the common difference of the given AP.

So, according to the question.

a₁₉ = 47

⇒ a + 18d = 47 ................(1)

Now, sum of the first n terms of an AP is given by :

Sn = n/2 {2a + (n - 1)d}

= 37/2 {2a + (37 - 1)d}

= 37/2 {2a + 36d}

= 37 {2a + 18d}

Substituting the value of a + 18d = 47 in the above, we get

=37 × 47

1739

So, the sum of the first 37 terms is 1739