## In an A.P. 17th term is 7 more than its 10th term. Find the common difference.

Given t17 = 7 + t10 …… (1)In t17, n = 17In t10, n = 10By using nth term of an A.P. formula, tn = a + (n – 1) dwhere n = number of termsa = first termd = common differencetn = nth termThus, on using formula in eq. (1) we get,⇒ a + (17 – 1) d = 7 + […]

## In the natural numbers from 10 to 250, how many are divisible by 4?

The number divisible by 4 in between 10 to 250 are12, 16, 20, 24, ………… 248From the above sequence, we havetn = 248, a = 12t1 = 16, t2 = 20Thus, d = t2 – t1 = 20 – 16 = 4Now, by using nth term of an A.P. formula tn = a + (n – 1) dwe can find value of […]

## 11, 8, 5, 2, . . . In this A.P. which term is number – 151?

By, given A.P. 11, 8, 5, 2, . . .we have a = 11, t1 = 8, t2 = 5Thus, d = t2 – t1 = 5 – 8 = – 3Given tn = – 151Now, by using nth term of an A.P. formula tn = a + (n – 1) dwe can find value of “n”Thus, on substituting all the value […]

## The 11th term and the 21st term of an A.P. are 16 and 29 respectively, then find the 41th term of that A.P.

## Find how many three-digit natural numbers are divisible by 5.

List of three-digit number divisible by 5 are100, 105, 110, 115, ………. 995Let us find how many such number are there?From the above sequence, we know thattn = 995, a = 100t1 = 105, t2 = 110Thus, d = t2 – t1 = 110 – 105 = 5Now, by using nth term of an A.P. formula that is tn = a + […]

## Find the 27th term of the following A.P.

Given A.P. is 9, 4, – 1, – 6, – 11, . . .Where first term a = 9Second term t1 = 4Third term t2 = – 1Common Difference d = t2 – t1 = – 1 – 4 = – 5We know that, nth term of an A.P. is tn = a + (n – 1) dWe need to find […]

## Find the 19th term of the following A.P.7, 13, 19, 25, . . .

Given A.P. is 7, 13, 19, 25, . . .Where first term a = 7Second term t1 = 13Third term t2 = 19Common Difference d = t2 – t1 = 19 – 13 = 6We know that, nth term of an A.P. istn = a + (n – 1) dWe need to find the 19th term,Here n = 19Thus, t19 = 7 + […]

## Given Arithmetic Progression 12, 16, 20, 24, . . . Find the 24th term of this progression.

Given A.P. is 12, 16, 20, 24, . . .Where first term a = 12Second term t1 = 16Third term t2 = 20Common Difference d = t2 – t1 = 20 – 16 = 4We know that, nth term of an A.P. is tn = a + (n – 1) dWe need to find the 24th term,Here n = 24Thus, t24 = 12 […]

## – 12, – 5, 2, 9, 16, 23, 30, . . .

Given A.P. is – 12, – 5, 2, 9, 16, 23, 30, . . .Here first term a = – 12Second term t1 = – 5Third term t2 = 2Common Difference d = t2 – t1 = 2 – (– 5) = 2 + 5 = 7We know that, nth term of an A.P. istn = a + (n – 1) […]

## Write the correct number in the given boxes from the following A. P.

(1) 1, 8, 15, 22, . . . Solution:Given 1, 8, 15, 22, . . .First term a = 1Second term t1 = 8Third term t2 = 15Fourth term t3 = 22We know that d = tn + 1 – tnThus, t2 – t1 = 15 – 8 = 7t3 – t2 = 22 – 15 = 7Thus, d = 7 (2) 3, […]