Question

The first term of an A.P. is 5 and the last term is 45. If the sum of all the
terms is 400, the number of terms is​

Answer 1

Answer:

The number of terms in the given A.P. is 16.

Step-by-step explanation:

First term=a=t1=5

Last term=tn=45.

Sum of terms=Sn=400.

We know,

$sn = \frac{n}{2} (t1 + tn)$

400=n/2 (5+45)

400×2=n×50

800=50n

800/50=n

80/5=n

n=16.

Hope it helps you.

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Answer 2

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

$\green{\tt{\therefore{Number\:of\:terms=16}}}$

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

$\green{\underline \bold{Fiven :}} \\ \tt: \implies First \: term( a_{1} ) = 5 \\ \\ \tt: \implies Last \: term( l) = 45 \\ \\ \tt: \implies Sum \: of \: nth \: term ( s_{n}) = 400 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Number \: of \: terms(n) = ?$

• According to given question :

$\bold{As \: we \: know\: that} \\ \tt: \implies s_{n} = \frac{n}{2} (2a + (n - 1)d) \\ \\ \tt: \implies s_{n} = \frac{n}{2} (a + a + (n - 1)d) \\ \\ \tt \circ \: l = a + (n - 1) d \\ \\ \tt: \implies s_{n} = \frac{n}{2}(a + l) \\ \\ \tt: \implies 400 = \frac{n}{2} (5 + 45) \\ \\ \tt: \implies 400 \times 2 = n \times 50 \\ \\ \tt: \implies \frac{400 \times 2}{50} = n \\ \\ \green{\tt: \implies n=16} \\ \\ \green{\tt \therefore Number \: of \: terms \: in \: ap \: s \: 16}$