Question

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.​

Answer 1

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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 .