Question

The first term of an ap is 5 and last term is 45.if the sum of the terms is 125,then find the number of term

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Total\:number\:of\:term=5}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies First \: term(a) = 5 \\ \\ \tt: \implies Last \: term(l) = 45 \\ \\ \tt: \implies Sum \: of \: n_{th} \: term( s_{n}) = 125 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Number \: of \: terms(n) = ?$

• According to given question :

AS WE KNOW THAT

$\tt: \implies s_{n} = \frac{n}{2} (a + a + (n - 1)d) - - - - - (1) \\ \\ \circ \: l = a + (n - 1)d \\ \\ \: \: 45 = a +( n - 1)d - - - - - (2)$

Putting the value of (2) in (1)

$\tt: \implies 125 = \frac{n}{2}(5 + 45) \\ \\ \tt: \implies 125 \times 2 = n \times 50 \\ \\ \tt: \implies \frac{250}{50} = n \\ \\ \green{\tt: \implies n = 5} \\ \\ \green{\tt\therefore Total \: number \: of \:terms = 5}$

Answer 2

Answer:

★ 5 terms ★

Step-by-step explanation:

Given:

• First term of AP is 5
• Last term of AP is 45
• Sum of term is s^n 125

To Find:

• Number of terms

Solution: Since, The term is given then we can use the formula

★ S^n = n/2 ( a + l ) ★

• a = 5
• l = 45
• sum is 125

† Putting all the given values in formula†

$\small\implies{\sf }$ 125 = n/2 ( 5 + 45 )

$\small\implies{\sf }$ 125 = n/2 x 50

$\small\implies{\sf }$ 125 x 2/50 = n

$\small\implies{\sf }$ 250/50 = n

$\small\implies{\sf }$ 5 = n

Hence, Number of term is 5