Question
Find the arithmetic progression whose third term is $16$ and seventh term exceeds its fifth term by $12$.
✓
Answer
Let $a , a + d , a +2 d, a +3 d$,........ be the $A.P.$
$a_n = a + (n – 1)d$
But $a_3 = 16$
$a_7 - a_5 = 12$
Now $a_3 = a + (3 - 1)d = a + 2d$
$a_5 = a + (5 - 1)d = a + 4d$
and $a_7 = a + (7 - 1)d = a + 6d$
$\therefore$ $a + 2d = 16$
$\Rightarrow a = 16 - 2d$
and $a_7 - a_5 = a + 6d - a - 4d$
$\Rightarrow\ 12 = 2\text{d}\Rightarrow \text{d}=\frac{12}{2}=6$
$\therefore$ $a = 16 - 2d = 16 - 2 \times 6$
$\Rightarrow a = 16 - 12 = 4$
$\therefore$ Sequencing ($A.P$.) will be
$4, 10, 16, 22, .....$
$a_n = a + (n – 1)d$
But $a_3 = 16$
$a_7 - a_5 = 12$
Now $a_3 = a + (3 - 1)d = a + 2d$
$a_5 = a + (5 - 1)d = a + 4d$
and $a_7 = a + (7 - 1)d = a + 6d$
$\therefore$ $a + 2d = 16$
$\Rightarrow a = 16 - 2d$
and $a_7 - a_5 = a + 6d - a - 4d$
$\Rightarrow\ 12 = 2\text{d}\Rightarrow \text{d}=\frac{12}{2}=6$
$\therefore$ $a = 16 - 2d = 16 - 2 \times 6$
$\Rightarrow a = 16 - 12 = 4$
$\therefore$ Sequencing ($A.P$.) will be
$4, 10, 16, 22, .....$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
When we toss a coin, there are two possible outcomes-Head or Tail. Therefore, the probability of each outcome is $\frac{1}{2}.$ Justify your answer.
→Write the family of quadratic polynomials having $-\frac{1}{4}$ and 1 as its zeros.
→A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is:
A spade.
A spade.
Two coins are tossed simultaneously. What is the probability of getting at least one head?
Prove the following trigonometric identities.
$(1-\cos^2\text{A})\text{cosec}^2\text{A}=1$
→$(1-\cos^2\text{A})\text{cosec}^2\text{A}=1$
D and E are points on the sides AB and AC respectively of a $\triangle\text{ABC}$ such that DE || BC: If AB = 13.3cm, AC = 11.9cm and EC = 5.1cm, find AD.
→Show that $( a - b )^2,\left( a ^2+ b ^2\right)$ and $( a + b )^2$ are in $A.P$?
→In two concentric circles, the radii are $OA = r \ cm$ and $OQ =6 \ cm,$ as shown in the figure. Chord $CD$ of larger circle is a tangent to smaller circle at $Q . PA$ is tangent to larger circle. If $PA =16 \ cm$ and $OP =20 \ cm,$ find the length $CD.$
→ Are the given numbers $1, 3, 9, 27, ........$ forms an $AP$? If It forms an $AP$, then find the common difference d and write the next three terms.
→What can you say about the prime factorisations of the $43$ of the following rationals:
$43.123456789$
→$43.123456789$