CameraIcon

SearchIcon

MyQuestionIcon

2

You visited us 2 times! Enjoying our articles? Unlock Full Access!

General Form of an AP

Question 3 vi...

Question

Question 3 (vi)
In an AP:
(vi) Given a = 2, d = 8, $S_{n} = 90$ , find n and $a_{n}$ .

Open in App

Solution

$G i v e n t h a t, a = 2, d = 8, S_{n} = 90 A s S_{n} = \frac{n}{2} [2 a + (n - 1) d] 90 = \frac{n}{2} [2 a + (n - 1) d] \Rightarrow 180 = n (4 + 8 n - 8) = n (8 n - 4) = 8 n^{2} - 4 n \Rightarrow 8 n^{2} - 4 n - 180 = 0 \Rightarrow 2 n^{2} - n - 45 = 0 \Rightarrow 2 n^{2} - 10 n + 9 n - 45 = 0 \Rightarrow 2 n (n - 5) + 9 (n - 5) = 0 \Rightarrow (2 n + 9) (n - 5) = 0 S o, n = 5 (a s i t i s a p o s i t i v e i n t e g e r) ∴ a_{5} = 2 + 8 \times 4 = 34$

Suggest Corrections

thumbs-up

1

Similar questions

Q. Question 3 (vii)
In an AP:
(vii) Given a = 8,

a_{n} = 62

S_{n} = 210

, find n and d.

Q. Question 3 (viii)
In an AP:
(viii) Given

a_{n} = 4

S_{n} = - 14

, find n and a.

a = 2, d = 8

S_{n}

= 90

n

a_{n}

Q. In an AP, given a

= 2

= 8

S_{n} = 90

a_{n}

Q. Question 3 (i)
In an AP:
(i) Given a = 5, d = 3,

a_{n} = 50

S_{n}

.

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

General Form of an AP

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon