5 th term of an arithmetic sequence is 7 and its 10 th tem is 32 . What is its common difference? What is its first term?
Answers
Answer:
Step-by-step explanation:
To find the common difference d, use the formula a1+4d=a5.
For us, a1 is 10 and a5 is 38.
10+4d=38
Now we can solve for d.
4d=28
d=7
Add the common difference to the first term to get the second term.
a2=a1+d=10+7=17
✪ Answer:
- Common difference = 5
- First term = -13
✪ Step-by-step explanation:
Given:
✯ 5th term of an AP = 7
✯ 10th term is 32
To find:
→ Common difference = ?
→ First term = ?
Solution:
We know that:
aₙ = a + (n - 1)d
where:
- 'aₙ' is the nth term
- 'a' is the first term
- 'n' is the number of terms
- 'd' is the common difference.
Since 5th term = 7,
a₅ = 7
⇒ a + (5 - 1)d = 7
⇒ a + 4d = 7 ----- [Equation ❶]
Similarly, 10th term = 32
a₁₀ = 32
⇒ a + (10 - 1)d = 32
⇒ a + 9d = 32 ----- [Equation ❷]
Now, [Equation ➁] - [Equation ➀]
a + 9d = 32
{-} a + 4d = 7
5d = 25
⇒ d = 25 ÷ 5
⇒ d = 5
∴ The common difference = 5
Now let's find the first term by substituting the value of 'd' in Equation ➀
➥ a + 4d = 7
↦ a + 4(5) = 7
↠ a + 20 = 7
⤇ a = 7 - 20
⇢ a = -13
∴ The first term = -13