Question

If the first term and the last term of a finite AP.are 5 and 95 respectively and d = 5, find n and Sn.

Answer 1

Dear Student,

Answer: n= 19 , Sn = 950

Solution:

ATQ first term 5, i.e a =5

let last term be nth term

95 = a+(n-1) d

d=5

95 = 5+ (n-1) 5

5 (n-1) =95-5

5(n-1) = 90

n-1 = 90/5

n-1 = 18

n = 18+1

n = 19.

Sum of n terms, if last term is given

Sn = n/2 (a+l)

Sn = 19/2 ( 5+95)

Sn =19/2(100)

Sn = 19(50)

Sn = 950

Hope it helps you.

Answer 2

Given First term of an AP a = 5, Last term l = 95 and common difference d = 5.

We know that Tn = a + (n - 1) * d

= > 95 = 5 + (n - 1) * 5

= > 95 = 5 + 5n - 5

= > 95 = 5n

= > n = 19

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Now,

Sum of the required series sn = (n/2)[a + l)

= > sn = (19/2)[5 + 95]

= > (19/2)[100]

= > 19 * 50

= > 950.

Hope this helps!