Question

the first tirm of ap is 5 the last term is 45 and the sum is 400 find the number of term and the common difference​

Answer 1

Answer:

n=16. d=8/3

Step-by-step explanation:

a=5

an=45

sn=400

n=?

d=?

sn=n/2(a+l)

400=n/2(5+45)

400=n/2(50)

400/50=n/2

8=n/2

8*2=n

16=n

an=a+(n-1)d

45=5+(16-1)d

45-5=15d

40=15d

40/15=d

8/3=d

Answer 2

Answer :

• Number of terms = 16
• Common difference = 2.6

S O L U T I O N :

Given,

• First term (a) = 5
• Last term (l) = 45
• Sum of terms (Sn) = 400

To Find,

• The number of terms and common difference.

Explanation,

Case (I), Number of terms,

We know that,

Sn = n/2 × (a + l)

[ Put the values ]

⇒ 400 = n/2 × (5 + 45)

⇒ 400 = n/2 × (50)

⇒ 400 = 25n

⇒ n = 400/25

⇒ n = 16

Case (II), Common difference,

We know that,

Sn = n/2 × (2a + (n - 1)d)

[ Here, n = 16 ]

⇒ S_16 = 16/2 × (2 × 5 + (16 - 1)d)

[ °.° S_16 = 400 ]

⇒ 400 = 8 × (10 + 16d - 1d)

⇒ 400 = 8 × (10 + 15d)

⇒ 400 = 80 + 120d

⇒ -120d = 80 - 400

⇒ -120d = -320

⇒ d = 2.6

Therefore,

The number of terms and common difference is 16 and 2.6 respectively.