the fifth term of an arithmetic sequence is 11 and the tenth is 41.what is the first term
Answers
“ Frist term(a) = - 13 ”.
Step-by-step explanation:
★ Given that :
◼ Fifth term of an AP : 11
- a5 = 11
◼ Tenth term of an AP: 41
- a10 = 41
★ To find :
◼ The first term (a).
★ Let :
➡ a5 : a + 4d = 11 ..... (1)
➡ a10 : a + 9d = 41 ..... (2)
- Subtract equations (1) & (2).
➡ - 5d = - 30
➡ d = -30/-5
➡ d = 6
- Substitute value of d in (1)
➡ a + 4(6) = 11
➡ a + 24 = 11
➡ a = 11 - 24
➡ a = - 13
★ Verification :
- Substitute the values of a & d in (1), to get LHS = RHS.
➡ - 13 + 4(6)
➡ - 13 + 24
➡ 11
☯ Since, LHS = RHS.
☯ Hence,it was verified.
∴ The first term (a) = - 13
SOLUTION
GIVEN
The fifth term of an arithmetic sequence is 11 and the tenth is 41
TO DETERMINE
The first term
CONCEPT TO BE IMPLEMENTED
If in an arithmetic progression
First term = a
Common difference = d
Then nth term of the AP
= a + ( n - 1 )d
EVALUATION
Let first term = a and common difference = d
Since the fifth term is 11
So by the given condition
a + 4d = 11 - - - - - - - - (1)
Again tenth term is 41
So by the given condition
a + 9d = 41 - - - - - - - - (2)
Equation 2 - Equation 1 gives
5d = 30
⇒ d = 6
From Equation 1 we get
a = 11 - 4d = 11 - 24 = - 13
First term = - 13
Common Difference = 6
FINAL ANSWER
First term = - 13
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