Advertisements
Advertisements
प्रश्न
Show that a1, a2, a3, … form an A.P. where an is defined as an = 3 + 4n. Also find the sum of first 15 terms.
Advertisements
उत्तर
an = 3 + 4n
a1 = 3 + 4 x 1 = 3 + 4 = 7
a2 = 3 + 4 x 2 = 3 + 8 = 11
a3 = 3 + 4 x 3 = 3 + 12 = 15
a4 = 3 + 4 x 4 = 3 + 16 = 19
and so on Here, a = 1 and d = 11 – 7 = 4
S15 = `n/(2)[2a + (n - 1)d]`
= `(15)/(2)[2 xx 7 + (15 - 1) xx 4]`
= `(15)/(2)[14 + 14 xx 14]`
= `(15)/(2)[14 + 56]`
= `(15)/(2) xx 70`
= 525.
APPEARS IN
संबंधित प्रश्न
An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term of the A.P.
In an AP given an = 4, d = 2, Sn = −14, find n and a.
Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.
If the sum of first m terms of an AP is ( 2m2 + 3m) then what is its second term?
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installment is Rs. 100 less than the previous one, find:
- amount of installments paid in the 9th month.
- total amount paid in the installment scheme.
In an AP, if Sn = n(4n + 1), find the AP.
Find the sum of the integers between 100 and 200 that are not divisible by 9.
Jaspal Singh repays his total loan of Rs. 118000 by paying every month starting with the first instalment of Rs. 1000. If he increases the instalment by Rs. 100 every month, what amount will be paid by him in the 30th instalment? What amount of loan does he still have to pay after the 30th instalment?
