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Find the sum of first 25 terms of following series whose the t

Question

Find the sum of first $25$ terms of following series whose the term is given:
$a_{n} = 3 + 4 n$

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Find the sum of first

25

terms of following series whose the term is given:

a_{n} = 3 + 4 n

15 mins ago

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15 mins ago

Text solutionVerified

Given

a_{n} = 3 + 4 n

.....(i)
Substituting various values of

n

in equation (i)

a_{1} = 3 + 4 (1) = 7

a_{2} = 3 + 4 (2) = 11

a_{3} = 3 + 4 (3) = 15, .......

Common difference

(d) = a_{2} - a_{1} = 11 - 7 = 4

a_{3} - a_{2} = 15 - 11 = 4

∵ a_{2} - a_{1} = a_{3} - a_{2} = 4

Thus series is

7, 11, 15, ....

and given series is an A.P
Here,

a = 7, d = 4

and

n = 25

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

S_{25} = \frac{25}{2} [2 \times 7 + (25 - 1) 4]

= \frac{25}{2} [14 + 24 \times 4]

= \frac{25}{2} [14 + 96]

= \frac{25}{2} \times 110

= 25 \times 55

= 1375

Thus

S_{25} = 1375

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Question Text	Find the sum of first $25$ terms of following series whose the term is given: $a_{n} = 3 + 4 n$
Answer Type	Text solution:1
Upvotes	150