Question

find the 25th term of AP 5,9/2,4, 7/2, 3.....​

Answer 1

Answer:-

The 25th term is -6.

Explanation:-

Given:-

• An AP 5, 9/2, 4, 7/2, 3....

To Find:-

• The 25th term of the AP.

Formulae Used:-

↦ d = a2 - a.

↦ an = a + (n-1)d.

Where,

• d = Commond difference.
• a2 = Second term.
• a = First term.
• n = Number of terms.
• an = nth term.

So Here,

• d = ??.
• a2 = 9/2.
• a = 5.
• n = 25.
• an (i.e. 25th term) = ?? [To Find].

Now,

Let us first find out the value of d.

↦ d = a2 - a.

↦ d = 9/2 - 5.

↦ d = (9-10)/2. (Taking LCM).

↦ d = -1/2.

So The Common Difference Of The AP Is -1/2.

So Lets find out the value of 25th term.

↦ an = a + (n-1)d.

↦ a25 = 5 + (25-1)(-1/2).

↦ a25 = 5 + (24)(-1/2).

↦ a25 = 5 + (-24/2).

↦ a25 = 5 + (-12).

↦ a25 = 5 - 12.

↦ a25 = -6.

Therefore The 25th Term Of The Given AP Is -6.

Answer 2

$\bf \large \underline \red{Answer : - }$

$\bf \underline \purple{Given : }$

• Given AP is 5,9/2,4,7/2,3....

$\bf \underline \purple{To \: \: find : }$

• 25 th term of AP!!!

$\bf \underline \purple{Formula \: \: used : }$

${\bf {\boxed {\underline{a_n = a+(n-1) d}}}}$

$\bf \underline \purple{Need \: \: to \: \: know : }$

$\bf \star \: a = first \: \: term \\ \\ \bf \star \:d = common \: \: difference \\ \\ \bf \star \:n = {n}^{th} \: \: term \:$

$\bf \large \underline \red{Solution : }$

$\star \: a_1 = 5 \\ \star \: a_2 = \frac{9}{2} \\ \star \: a_3 = 4 \\ \star \: a_4 = \frac{7}{2} \\ \star \: a_5 = 3$

First find out the common difference:-

$\bf \large \: d = a_2 \: - a_1$

$\bf \large \: d = \frac{9}{2} - 5 \\ \\ \bf \large \: d = \frac{9 - 10}{2} \\ \\ \bf \large \: d = \frac{ - 1}{2}$

Now, find 25 th term of AP!!!

$\bf \large \implies \: a_{25} = a + (n - 1)d \\ \\ \bf \large \implies \: a_{25} =5 + (25 - 1) \frac{ - 1}{2} \\ \\ \bf \large \implies \: a_{25} =5 + (24) \frac{ - 1}{2} \\ \\ \bf \large \implies \: a_{25} =5 - \frac{24}{2} \\ \\ \bf \large \implies \: a_{25} =5 - 12 \\ \\ \bf \large \implies \: a_{25} = - 7$

$\bf \large \: \therefore \: {25}^{ \: th} \: \: term \: \: of \: \: AP \: \: is \: \: \pink{ - 7}$