Question

if the sum of first 8 terms of an AP is 292 and the sum of its first 12 term is 606 find the 21st term​

Answer 1

Answer:

21st term = 152

Step-by-step explanation:

Sum^n = n/2(2a + (n-1)d)

Sum⁸ = 292

292 = 8/2(2a + (8-1)d

292 = 4(2a+ 7d)

2a + 7d = 73

2a = 73 - 7d eq1

Sum¹² = 606

606 = 12/2(2a + (12-1)d)

606 = 6(2a + 11d)

2a + 11d = 101

2a = 101 - 11d eq2

73 - 7d = 101 - 11d

4d = 28

d = 7

put the value of d = 7 in any of the equation

I am putting in eq1

2a = 73 - 7×7

2a = 73 - 49

2a = 24

a = 12

21st term = a + 20d

12 + 20 × 7 = 12 + 140 = 152