Question

The sum of first 7 term of an AP is 63 and sum of its next 7 term is 161. Find 28th term of AP

Answer 1

Answer:

this is the correct answer

Step-by-step explanation:

4.17

Answer 2

Given:-

• Sum of first 7th term = 63
• Sum of next 7th term = 161

To find:-

• Find the 28th term of Ap..?

Solutions:-

• Sn = n/2 [2a + (n - 1)d]

Therefore,

=> S7 = 7/2 [2a + (7 - 1)d]

=> 7/2 (2a + 6d) = 63

=> 7/2 × 2 (a + 3d) = 63

=> 7(a + 3d) = 63

=> a + 3d = 63/7

=> a + 3d = 9 ...........(i).

Therefore,

Sum of next 7th term = 161

Sum of 14th term = 224

=> S14 = 14/2 [2a + (14 - 1)d]

=> 14/2 (2a + 13d) = 224

=> 7 × (2a + 13d) = 224

=> (a + 3d) = 224/7

=> a + 13d = 32 ...........(ii).

Multiplying Eq. (i). by 2. We get.

=> 2a + 6d = 18 ..........(iii).

Now, Subtracting Eq. (iii) and (ii) we get,

${2a} \: + \: {6d} \: \: = \: \: {18} \\ {2a} \: + \: {13d} \: \: = \: \: {32} \\ \underline{ - \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: = \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: {7d} \: \: \: \: \: \: \: \: = \: \: \: {14}$

=> d = 14/7

=> d = 2

Now, putting the value of d in Eq. (i).

=> a + 3d = 9

=> a + 3 × 2 = 9

=> a + 6 = 9

=> a = 9 - 6

=> a = 3

So, the 28th term of Ap.

=> a28 = a + 27d

=> a28 = 3 + 27 × 2

=> a28 = 3 + 54

=> a28 = 57

Hence, the 28th term of the Ap is 57.