Question

1. Let S16 = 936 and first team is 21, then
What will be the 23rd term?​

Answer 1

Answer:

The 23rd term of the AP is 131.

Step-by-step-explanation:

We have given that the sum of first 16 terms of AP is 936 i. e. $\sf\:S_{16}\:=\:936$ and first term of AP is 21 i. e. $\sf\:a\:=\:21$.

We have to find 23rd term of AP i. e. $\sf\:t_{23}$.

We know that,

$\sf\:S_{n}\:=\:\frac{n}{2}\:[\:2a\:+\:(\:n\:-\:1\:)\:d\:]\:\:\:-\:-\:[\:Formula\:]\\\\\implies\sf\:S_{16}\:=\:\frac{\cancel{16}}{\cancel2}\:[\:2\:\times\:21\:+\:(\:16\:-\:1\:)\:\times\:d\:]\\\\\implies\sf\:936\:=\:8\:[\:42\:+\:15\:d\:]\\\\\implies\sf\:\cancel{\frac{936}{8}}\:=\:42\:+\:15d\\\\\implies\sf\:117\:=\:42\:+\:15d\\\\\implies\sf\:15d\:=\:117\:-\:42\\\\\implies\sf\:15d\:=\:75\\\\\implies\sf\:d\:=\:\cancel{\frac{75}{15}}\\\\\implies\boxed{\red{\sf\:d\:=\:5}}$

Now,

$\sf\:t_{n}\:=\:a\:+\:(\:n\:-\:1\:)\:d\:\:\:-\:-\:-\:[\:Formula\:]\\\\\implies\sf\:t_{23}\:=\:21\:+\:(\:23\:-\:1\:)\:\times\:5\\\\\implies\sf\:t_{23}\:=\:21\:+\:22\:\times\:5\\\\\implies\sf\:t_{23}\:=\:21\:+\:110\\\\\implies\boxed{\red{\sf\:t_{23}\:=\:131}}$

Additional Information:

1. Arithmetic Progression:

1. In a sequence, if the common difference between two consecutive terms is constant, then the sequence is called as Arithmetic Progression ( AP ).

2. $\sf\:n^{th}$ term of an AP:

The number of a term in the given AP is called as $\sf\:n^{th}$ term of an AP.

3. Formula for $\sf\:n^{th}$ term of an AP:

$\sf\:t_{n}\:=\:a\:+\:(\:n\:-\:1\:)\:d$

4. The sum of the first n terms of an AP:

The addition of either all the terms of a particular terms is called as sum of first n terms of AP.

5. Formula for sum of the first n terms of A. P. :

$\boxed{\red{\sf\:S_{n}\:=\:\frac{n}{2}\:[\:2a\:+\:(\:n\:-\:1\:)\:d\:]}}$