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Find the sum of first 15 terms of an A.P. whose 5th and 9th te

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Find the sum of first 15 terms of an A.P. whose 5th and 9th terms are 26 and 42 respectively

570

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Text solutionVerified

Given an AP:

Fifth term,

a_{5} = 26

Nineth term,

a_{9} = 42

To find:

Sum of first

15

terms of the AP

n^{t h}

term of AP is given by:

a_{n} = a + (n - 1) d

a_{5} = 26 = a + (5 - 1) d ............... (i)

a_{9} = 42 = a + (9 - 1) d ............... (ii)

Subtracting (i) from (ii), we get

16 = 4 d

d = 4

Substituting value of

d

in (i), we get

26 = a + 4 \times 4

a = 10

Now, sum of first

n

terms is given by:

S_{n} = \frac{n}{2} (2 a + (n - 1) d)

Substituting values, we get sum of fifteen terms as

S_{15} = \frac{15}{2} (2 \times 10 + (15 - 1) \times 4)

S_{15} = 570

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Question Text	Find the sum of first 15 terms of an A.P. whose 5th and 9th terms are 26 and 42 respectively
Answer Type	Text solution:1
Upvotes	152