Question

find the sum of the arithmetic sequence 5,8,11,...,200​

Answer 1

Answer:

To find the sum of series is

S = n/2(a+l)

S: sum of terms

n: no. of terms

a: 1st term

l: last term

To find no. of terms

l=a+(n-1)d (d: common difference)

200=5+(n-1)3

195=3n-3

198=3n

66=n

S= 66/2(5+200)

S= 33(205)

S=6765

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Answer 2

AnswEr :-

• The sum of the arithmetic sequence is 6600.

Given :-

• An AP as 5, 8, 11......200

To Find :-

• Sum of the arithmetic sequence.

SoluTion :-

Here,

• First term a = 5

• Second term = 8

• Common difference d = 8 - 5 = 3

• nth term of the AP Tn = 200

» Tn = a + (n - 1)d

→ 200 = 5 + (n - 1)3

→ 200 = 5 + 3n - 3

→ 200 = 2 + 3n

→ 200 - 2 = 3n

→ 198 = 3n

→ n = 198/3

→ n = 66

Now, we'll find the sum of the n terms :-

» Sn = n/2 [a + (n - 1)d ]

→ Sn = 66/2 [ 5 + (66 - 1)3 ]

→ Sn = 33 [ 5 + 195 ]

→ Sn = 33 × 200

→ Sn = 6600

Hence, the sum of the arithmetic sequence is 6600.

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