The sum of the first 7 terms of an A.P. is 63 and the sum of its next

1.	The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.
Answer» S₇ = 63 \(\frac{7}{2}\)[2(a) + 6d] = 639 a + 3d = 9 (i) a₈ = a + 7d Hence, for next 7 terms first term will be the 8^th term i.e. a + 7d Sum of next 7 terms, S’₇ = \(\frac{7}{2}\)[2(a + 7d) + 6d] 161 = 7 [a + 7d + 3d] 23 = a + 10d 23 = 9 – 3d + 10d [From (i)] 14 = 7d d = 2 Putting the value of d in (i), we get A = 9 – 3(2) = 3 Now, a₂₈= a + 27d = 3 + 27(2) = 3 + 54 = 57

The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

Answer»

S₇ = 63

\(\frac{7}{2}\)[2(a) + 6d] = 639

a + 3d = 9 (i)

a₈ = a + 7d

Hence, for next 7 terms first term will be the 8^th term i.e. a + 7d

Sum of next 7 terms, S’₇ = \(\frac{7}{2}\)[2(a + 7d) + 6d]

161 = 7 [a + 7d + 3d]

23 = a + 10d

23 = 9 – 3d + 10d [From (i)]

14 = 7d

d = 2

Putting the value of d in (i), we get

A = 9 – 3(2) = 3

Now, a₂₈= a + 27d

= 3 + 27(2)

= 3 + 54

= 57