QQuestion
The 5th term and the 9th term of an Arithmetic Progression are 4 and −12 respectively. Find:
(a) the first term
(b) the common difference
(c) the sum of 16 terms of the A.P.
✓Answer
Let the first term be a and the common difference be d.
The nth term of an A.P. is:
an = a + (n − 1)d
Given, the 5th term is 4:
⇒ a + (5 − 1)d = 4
⇒ a + 4d = 4 … (1)
Given, the 9th term is −12:
⇒ a + (9 − 1)d = −12
⇒ a + 8d = −12 … (2)
Subtracting (1) from (2):
⇒ (a + 8d) − (a + 4d) = −12 − 4
⇒ a + 8d − a − 4d = −16
⇒ 4d = −16
⇒ d = −4
Substituting d = −4 in (1):
⇒ a + 4(−4) = 4
⇒ a − 16 = 4
⇒ a = 20
(a) Therefore, the first term is 20.
(b) The common difference is −4.
(c) Sum of n terms: Sn = \frac{n}{2}[2a+(n-1)d]
⇒ S16 = \frac{16}{2}[2(20)+(16-1)(-4)]
⇒ S16 = 8[40 − 60]
⇒ S16 = 8(−20)
Therefore, S16 = −160.
Related Questions
More ICSE Easy level questions
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 − n). Find: (a) its first term and common difference. (b) the sum of its first 25 terms.
The first term of an Arithmetic Progression is 5, the last term is 50 and the sum is 440. Find:(a) the number of terms.(b) the common difference.
15, 30, 60, 120, ... are in G.P. (a) Find the nth term of this G.P. in terms of n. (b) How many terms of the above G.P. will give the sum 945?
What number must be added to each of the numbers 4, 6, 8 and 11 so that the resulting four numbers are in proportion?
A bag contains 25 cards numbered from 1 to 25. A card is drawn at random. Find the probability that the number on the card drawn is: (a) a multiple of 5 (b) a perfect square (c) a prime number.
The following distribution gives the daily wages of 60 workers of a factory: Daily income (₹) Number of workers 200–300 6 300–400 10 400–500 14 500–600 16 600–700 10 700–800 4 Use graph paper. Take 2 cm = ₹100 along one axis and 2 cm = 2 workers along the other axis. Draw a histogram and hence find the mode of the distribution.
Using componendo and dividendo, solve for x: = 3
The following table gives the marks scored by a set of students in an examination. Calculate the mean of the distribution using the shortcut method. Marks Number of students (f) 0–10 3 10–20 8 20–30 14 30–40 9 40–50 4 50–60 2
Solve the following inequation. Write down the solution set and represent it on the real number line. − 5(x − 9) ≥ 17 − 9x > x + 2, x ∈ R.
ABC is a triangle whose vertices are A(1, −1), B(0, 4) and C(−6, 4). D is the midpoint of BC. Find: (a) the coordinates of D (b) the equation of the median AD.
Which term of the Arithmetic Progression 15, 30, 45, 60, ... is 300? Hence, find the sum of all the terms of the A.P. up to 300.
Mrs. Arora bought the following articles from a departmental store: S.No. Item Price Rate of GST Discount 1 Hair oil ₹1200 18% ₹100 2 Cashew nuts ₹600 12% — Find: (a) the total GST paid (b) the total bill amount including GST.