If first term of an AP is 5 and the 10th term is 45, then sum of first ten
terms of the AP is
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Answer:
EXPLANATION.
GIVEN
First term of an Ap = 5
10th term of an Ap = 45
To find Sum of ten terms of an Ap
according to the question,
Formula of nth term of an Ap
\bigstar\blue{\boxed{\bold{a_{n} \: = a + ( n \: - 1)d}}}★
a
n
=a+(n−1)d
First term = a = 5
T10 = 45
a + 9d = 45
put the value of a in T10 term
5 + 9d = 45
9d = 40
d = 40/9
To find sum of ten terms
Formula of sum of nth terms
\bigstar\orange{\boxed{\bold{s_{n} \: = \frac{n}{2}(2a \: + (n - 1)d)} }}★
s
n
=
2
n
(2a+(n−1)d)
\bold{s_{10} \: = \frac{10}{2} (2(5) + 9 \times \frac{40}{9} )}s
10
=
2
10
(2(5)+9×
9
40
)
5 ( 10+ 40 )
5 ( 50) = 250
Therefore,
sum of 10th term of an Ap = 250
Step-by-step explanation:
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