Lesson Example Discussion Quiz: Class Homework |
Step-3 |
Title: Consecutive terms of A.P |
Grade: 9-a Lesson: S4-L5 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
If the sum of first 8 terms of an A.P. is 64 and that of its first 18 terms is 324, find the sum of first n terms of the A.P. |
|
2 |
Step |
Sum of first 8 terms |
\$S_8 = 64\$ |
3 |
Step |
Sum of first 18 terms |
\$S_18 = 324\$ |
4 |
Formula: |
We know that sum of n terms of A.P. is |
\$ S_n = n/2(2a + (n-1)d)\$ |
5 |
Step |
Sum of 8 terms of A.P. |
\$ S_8 = 8/2(2a + (8-1)d)\$ |
6 |
Step |
Substitute the value of \$S_8\$ |
\$ 64 = 4(2a + 7d) \$ |
7 |
Step |
After simplification |
\$ \cancel64^16/\cancel4 = 2a + 7d \$ |
8 |
Step |
After cancellation |
\$ 2a + 7d = 16 -> (1)\$ |
9 |
Step |
Sum of 18 terms of A.P. |
\$ S_18 = 18/2(2a + (18-1)d)\$ |
10 |
Step |
Substitute the value of \$S_18\$ |
\$ 324 = 9(2a + 17d) \$ |
11 |
Step |
After simplification |
\$ \cancel324^36/\cancel9^1 = 2a + 17d \$ |
12 |
Step |
After cancellation |
\$ 2a + 17d = 36 -> (2)\$ |
13 |
Step |
Subtracting equation (1) from equation (2) |
\$2a + 17d - (2a + 7d) = 36 - 16\$ |
14 |
Step |
After subtraction |
\$ 2a + 17d - 2a - 7d = 20\$ |
15 |
Step |
After simplification |
\$ \cancel10^1d = \cancel20^2\$ |
16 |
Step |
After cancellation |
\$ d = 2\$ |
17 |
Step |
Substitute d value in \$eq^n (1)\$ |
\$ 2a + 7(2) = 16 \$ |
18 |
Step |
After simplification |
\$ 2a + 14 = 16 \$ |
19 |
Step |
After simplification |
\$ 2a = 16 - 14 = 2 \$ |
20 |
Step |
After simplification |
\$ a = \cancel2^1/\cancel2^1 \$ |
21 |
Step |
After simplification |
\$ a = 1\$ |
22 |
Step |
Sum of n terms of A.P. is |
\$S_n = n/2(2a + (n-1)d) \$ |
23 |
Step |
Substitute a,d values |
\$S_n = n/2(2(1) + (n-1)2) \$ |
24 |
Step |
After simplification |
\$S_n = n/2(\cancel2 + 2n - \cancel2) \$ |
25 |
Step |
After simplification |
\$S_n = n/\cancel2( \cancel2n ) \$ |
26 |
Step |
After simplification |
\$S_n = n^2 \$ |
27 |
Answer |
D |
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Tutor: Questions
| Seq | Type | Question | Audio |
|---|---|---|---|
1 |
Problem |
What did you learn from this problem? |
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2 |
Clue |
What did you learn from the clues? |
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3 |
Hint |
What did you learn from the Hints? |
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4 |
Step |
What did you learn from the Steps? |
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5 |
Step |
How can we improve the Steps? |
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