Advertisements
Advertisements
Questions
The 4th term of an A.P. is 22, and the 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series to 8 terms.
The 4th term of an A.P. is 22, and the 15th term is 66. Find the sum of its 8 terms.
Advertisements
Solution
Let a be the first term and d be the common difference of the given A.P.
Now,
4th term = 22
⇒ a + 3d = 22 ...(i)
15th term = 66
⇒ a + 14d
= 66
Subtracting (i) from (ii), we have
11d = 44
⇒ d = 4
Substituting the value of d in (1), we get
a = 22 − 3 × 4
= 22 − 12
=10
⇒ First term = 10
Now
Sum of 8 terms = `8/2[2xx10+7xx4]`
= 4[20 + 28]
= 4 × 48
= 192
APPEARS IN
RELATED QUESTIONS
Solve for x : ` 2x^2+6sqrt3x-60=0`
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
48x² – 13x -1 = 0
Complete the following activity to find the value of discriminant for quadratic equation 4x2 – 5x + 3 = 0.
Activity: 4x2 – 5x + 3 = 0
a = 4, b = ______, c = 3
b2 – 4ac = (–5)2 – (______) × 4 × 3
= ( ______ ) – 48
b2 – 4ac = ______
Find the sum of the roots of the equation x2 – 8x + 2 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
2x2 + x – 1 = 0
Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
