Question

Find the sum 25,28,31,------- 100​

Answer 1

Given :-

• First term = a = 25
• Common difference = d = 28 - 25 = 3
• Last term = aₙ = 100

To find :-

Sum of n terms = Sₙ

Solution :-

Step 1: Firstly, find out the number of terms (n) in this A.P.

aₙ = a + (n - 1)d

⇒ 100 = 25 + (n - 1)3

⇒ 100 - 25 = 3 (n - 1)

⇒ 3 (n - 1) = 75

⇒ (n - 1) = 25

⇒ n = 26

Step 2: Sₙ can be found out by applying the formula:

Sₙ = n ÷ 2 (a + aₙ)

⇒ Sₙ = 26 ÷ 2 (25 + 100)

⇒ Sₙ = 13 (125)

⇒ Sₙ = 1625

∴ Sum of n terms of this particular A.P = 1625

KNOW MORE:

• Sum of n terms can also be given as:

Sₙ = n/2 (2a + (n - 1)d)

Answer 2

$\sf\huge\bold{Answer:}$

Given :

Series : 25,28,31,..., 100

To find :

Sum of all the terms in series

Solution :

Firstly, let us prove that the series forms an AP

i.e. d1=d2

Series : 25,28,31,..., 100

a1=25

a2=28

a3=31

d1=a2-a1=28-25=3

d2=a3-a2=31-28=3

d1=d2

Since, common difference is same between each terms, the above series forms an AP

AP : 25,28,31,..., 100

a1=25

a2=28

a3=31

a(n)=100

d=3

• To find number of terms (n) in an AP

a(n)=a+(n-1)d

100=25+(n-1)3

100-25=3n-3

75+3=3n

78=3n

78/3=n

26=n

n=26

» Total terms in AP are 26.

• Sum of all terms in AP

Sn=n/2[2a+(n-1)d] $\: \:$ {Sum for n terms}

Sn=26/2[2×25+(26-1)3]

Sn=13[50+25×3]

Sn=13[50+75]

Sn=13[125]

Sn=13×125

Sn=1625

Sn=1625

Sum of terms in AP = 1625