Math, asked by Aditi2207, 7 months ago

The 4th term of an A.P. is 22 and 15th term is 66. Find the first term and the common difference. Hence, find the sum of first 8 terms of the A.P.​

Answers

Answered by Anonymous
60

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Given :-

  • 4th term of AP = 22
  • 15th term of AP = 66

To Find :-

  • 8th term of AP

Therefore :-

  • (a)4 = 22
  • a + 3d = 22 \:  \:  \:  \:  \:  \:  .....1st \: eq .
  • (a)15 = 66
  • a -  14d = 66 \:  \:  \:  \:  \:  \:  \:  \: 2nd \: eq.

From 1st and 2nd equation :-

  • we get

➡a - 14d = 66 [ equation 1 ]

➡a + 3 d = 22 [equation 2]

  • 11 d = 44
  • d =  \frac{44}{11}
  • d = 4

Put d = 4 in equation 1

  • a + 3(4)=22
  • a = 22- 12
  • a = 10

Now :-

(s)8 =  \frac{8}{2} (2(10) + (8 - 1)4)

(s)8 = 4(20 + 28)

(s)8 = 4(48)

(s)8 = 192

Final answer is 192 .

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